Assignment_1_DS.ipynb

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      "name": "Copy of Assignment -1 - DS.ipynb",
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hmr2U-GChnlR",
        "colab_type": "text"
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      "source": [
        "\n",
        "# **Assignment - 1 : Getting Started**\n",
        "\n",
        "---\n",
        "\n",
        "This assignment will get you familiarized with python libraries required for ***data science*** and ***machine learning***. You will have to complete the code snippets and run them. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "211pD45xEO0u",
        "colab_type": "text"
      },
      "source": [
        "## **Note :**   Use only the methods and attributes of the ```numpy``` library. **Do not** hard-code them. Avoid loops as much as possible."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e_B03izqYAWf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import seaborn as sns\n",
        "import scipy.stats as stats\n",
        "from matplotlib import pyplot as plt\n",
        "from math import pi"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O7v9C4mun3SQ",
        "colab_type": "text"
      },
      "source": [
        "---\n",
        "## Part - 1\n",
        " In this part, you will work with the library ```numpy```. \n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "846yDaXQwiMD",
        "colab_type": "text"
      },
      "source": [
        "Import ```numpy``` with an alias name ```np```. Initialize two arrays $a$, $b$ of size $3 \\times 5$ with random values and print them. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_MyeCO3_o3oq",
        "colab_type": "code",
        "outputId": "8388a2ea-1156-4260-ba13-bc71f318dd2c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        }
      },
      "source": [
        "import numpy as np\n",
        "a=np.random.random_sample((3, 5))\n",
        "print(\"a = {}\".format(a))\n",
        "b=np.random.random_sample((3, 5))\n",
        "print(\"b = {}\".format(b))\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "a = [[0.57019677 0.43860151 0.98837384 0.10204481 0.20887676]\n",
            " [0.16130952 0.65310833 0.2532916  0.46631077 0.24442559]\n",
            " [0.15896958 0.11037514 0.65632959 0.13818295 0.19658236]]\n",
            "b = [[0.36872517 0.82099323 0.09710128 0.83794491 0.09609841]\n",
            " [0.97645947 0.4686512  0.97676109 0.60484552 0.73926358]\n",
            " [0.03918779 0.28280696 0.12019656 0.2961402  0.11872772]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p7jtpYT4wiO6",
        "colab_type": "text"
      },
      "source": [
        "Initialize and print two arrays $c$ and $d$ having the following properties:\n",
        "*   $c$ is a row vector with all non-negative integer values less than 100\n",
        "* $d$ is a square matrix of size 3 having all entries as 0.0"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Pl5tQpAFIa93",
        "colab_type": "code",
        "outputId": "d0ec1569-f323-4908-df75-f9c669720c10",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 170
        }
      },
      "source": [
        "c= np.arange(100)\n",
        "print(\"c = {}\".format(c))\n",
        "print(\"-\"*20)\n",
        "d = np.zeros((3,3))\n",
        "print('d = {}'.format(d))\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "c = [ 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\n",
            " 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47\n",
            " 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71\n",
            " 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95\n",
            " 96 97 98 99]\n",
            "--------------------\n",
            "d = [[0. 0. 0.]\n",
            " [0. 0. 0.]\n",
            " [0. 0. 0.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qqgtSsa88Zmh",
        "colab_type": "text"
      },
      "source": [
        "We have $e$ as following : ```e = [[1,2,3],[4,5,6],[7,8,9]]```. Change $e$ as a numpy array and print it."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Krhm4bVE7RET",
        "colab_type": "code",
        "outputId": "aa2b0206-4244-464a-9f66-6a4d8d00b165",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        }
      },
      "source": [
        "e = [[1,2,3],[4,5,6],[7,8,9]]\n",
        "np.asarray(e)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2, 3],\n",
              "       [4, 5, 6],\n",
              "       [7, 8, 9]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 70
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1qTikI0foam9",
        "colab_type": "text"
      },
      "source": [
        "$f$ and $g$ are two square matrices of size 5 such that all the entries of $f$ are 1 and $g$ is an identity matrix. Initialize them and print them"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DvaLckI49aBV",
        "colab_type": "code",
        "outputId": "737507cf-4299-4b0a-eccb-77aae424c05b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 187
        }
      },
      "source": [
        "f=np.ones((5,5), dtype=np.int16 )\n",
        "print('f = {}'.format(f))\n",
        "g=np.eye(5,5)\n",
        "print('g = {}'.format(g))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "f = [[1 1 1 1 1]\n",
            " [1 1 1 1 1]\n",
            " [1 1 1 1 1]\n",
            " [1 1 1 1 1]\n",
            " [1 1 1 1 1]]\n",
            "g = [[1. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 0. 1.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gcBZAZibAKcg",
        "colab_type": "text"
      },
      "source": [
        "Reshape $c$ into a $10 \\times 10$ matrix and name it $h$. Now flatten $h$, call it $c^\\prime$ and print **YES** when the shapes of $c$ and $c^\\prime$ are same. Otherwise print **NO**."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I71vtO9bA9Pi",
        "colab_type": "code",
        "outputId": "2e16349f-cb62-42c8-b3dd-225fdeec8fa4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 289
        }
      },
      "source": [
        "h=c.reshape(10,10)\n",
        "print(\"h = {}\".format(h))\n",
        "c_bar = h.flatten()\n",
        "print(\"c_bar = {}\".format(c_bar))\n",
        "c_bar.shape\n",
        "print(c_bar.shape==c.shape)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "h = [[ 0  1  2  3  4  5  6  7  8  9]\n",
            " [10 11 12 13 14 15 16 17 18 19]\n",
            " [20 21 22 23 24 25 26 27 28 29]\n",
            " [30 31 32 33 34 35 36 37 38 39]\n",
            " [40 41 42 43 44 45 46 47 48 49]\n",
            " [50 51 52 53 54 55 56 57 58 59]\n",
            " [60 61 62 63 64 65 66 67 68 69]\n",
            " [70 71 72 73 74 75 76 77 78 79]\n",
            " [80 81 82 83 84 85 86 87 88 89]\n",
            " [90 91 92 93 94 95 96 97 98 99]]\n",
            "c_bar = [ 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\n",
            " 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47\n",
            " 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71\n",
            " 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95\n",
            " 96 97 98 99]\n",
            "True\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8FrecDPiA-Bv",
        "colab_type": "text"
      },
      "source": [
        "Let $A$ denote a randomly initialized three dimensional matrix of shape (2,10,5). Transpose $A$, call it $A^\\prime$, such that its shape is (5,2,10) and print it."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VbOKqSm6Bkaq",
        "colab_type": "code",
        "outputId": "0871d4da-5aed-4a07-8a8c-57ccfebd3f4b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 799
        }
      },
      "source": [
        "A = np.random.rand(2,10,5)\n",
        "print(A)\n",
        "A_bar = np.transpose(A,(2,0,1))\n",
        "print(A_bar)\n",
        "print(A_bar.shape)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[[0.31798318 0.41426299 0.0641475  0.69247212 0.56660145]\n",
            "  [0.26538949 0.52324805 0.09394051 0.5759465  0.9292962 ]\n",
            "  [0.31856895 0.66741038 0.13179786 0.7163272  0.28940609]\n",
            "  [0.18319136 0.58651293 0.02010755 0.82894003 0.00469548]\n",
            "  [0.67781654 0.27000797 0.73519402 0.96218855 0.24875314]\n",
            "  [0.57615733 0.59204193 0.57225191 0.22308163 0.95274901]\n",
            "  [0.44712538 0.84640867 0.69947928 0.29743695 0.81379782]\n",
            "  [0.39650574 0.8811032  0.58127287 0.88173536 0.69253159]\n",
            "  [0.72525428 0.50132438 0.95608363 0.6439902  0.42385505]\n",
            "  [0.60639321 0.0191932  0.30157482 0.66017354 0.29007761]]\n",
            "\n",
            " [[0.61801543 0.4287687  0.13547406 0.29828233 0.56996491]\n",
            "  [0.59087276 0.57432525 0.65320082 0.65210327 0.43141844]\n",
            "  [0.8965466  0.36756187 0.43586493 0.89192336 0.80619399]\n",
            "  [0.70388858 0.10022689 0.91948261 0.7142413  0.99884701]\n",
            "  [0.1494483  0.86812606 0.16249293 0.61555956 0.12381998]\n",
            "  [0.84800823 0.80731896 0.56910074 0.4071833  0.069167  ]\n",
            "  [0.69742877 0.45354268 0.7220556  0.86638233 0.97552151]\n",
            "  [0.85580334 0.01171408 0.35997806 0.72999056 0.17162968]\n",
            "  [0.52103661 0.05433799 0.19999652 0.01852179 0.7936977 ]\n",
            "  [0.22392469 0.34535168 0.92808129 0.7044144  0.03183893]]]\n",
            "[[[0.31798318 0.26538949 0.31856895 0.18319136 0.67781654 0.57615733\n",
            "   0.44712538 0.39650574 0.72525428 0.60639321]\n",
            "  [0.61801543 0.59087276 0.8965466  0.70388858 0.1494483  0.84800823\n",
            "   0.69742877 0.85580334 0.52103661 0.22392469]]\n",
            "\n",
            " [[0.41426299 0.52324805 0.66741038 0.58651293 0.27000797 0.59204193\n",
            "   0.84640867 0.8811032  0.50132438 0.0191932 ]\n",
            "  [0.4287687  0.57432525 0.36756187 0.10022689 0.86812606 0.80731896\n",
            "   0.45354268 0.01171408 0.05433799 0.34535168]]\n",
            "\n",
            " [[0.0641475  0.09394051 0.13179786 0.02010755 0.73519402 0.57225191\n",
            "   0.69947928 0.58127287 0.95608363 0.30157482]\n",
            "  [0.13547406 0.65320082 0.43586493 0.91948261 0.16249293 0.56910074\n",
            "   0.7220556  0.35997806 0.19999652 0.92808129]]\n",
            "\n",
            " [[0.69247212 0.5759465  0.7163272  0.82894003 0.96218855 0.22308163\n",
            "   0.29743695 0.88173536 0.6439902  0.66017354]\n",
            "  [0.29828233 0.65210327 0.89192336 0.7142413  0.61555956 0.4071833\n",
            "   0.86638233 0.72999056 0.01852179 0.7044144 ]]\n",
            "\n",
            " [[0.56660145 0.9292962  0.28940609 0.00469548 0.24875314 0.95274901\n",
            "   0.81379782 0.69253159 0.42385505 0.29007761]\n",
            "  [0.56996491 0.43141844 0.80619399 0.99884701 0.12381998 0.069167\n",
            "   0.97552151 0.17162968 0.7936977  0.03183893]]]\n",
            "(5, 2, 10)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xR2zd-nkCani",
        "colab_type": "text"
      },
      "source": [
        "You have a matrix $X$ of size (10,5) filled with random values. Print the following :\n",
        "* Minimum value and index where it occured, for each column\n",
        "* Maximum value and the index where it occured, for each column\n",
        "* Minimum value and index where it occured, for each row\n",
        "* Maximum value and index where it occured, for each row\n",
        "* Minimum value and index where it occured, for the entire matrix\n",
        "* Maximum value and index where it occured, for the entire matrix"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FR2Wd4fWD_Og",
        "colab_type": "code",
        "outputId": "b351ef30-68c3-4fe7-8da4-85b45f42a91d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "np.random.seed(0)\n",
        "X = np.random.rand(10,5)\n",
        "X\n",
        "\n",
        "# Minimum and Maximum values of each row, column and entire matrix X\n",
        "X.max(0)\n",
        "X.min(0)\n",
        "X.max(1)\n",
        "X.min(1)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.4236548 , 0.38344152, 0.07103606, 0.0202184 , 0.11827443,\n",
              "       0.14335329, 0.0187898 , 0.61209572, 0.06022547, 0.1289263 ])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YpjW2ypkEGtS",
        "colab_type": "text"
      },
      "source": [
        "Find and print the following for the matrix X: \n",
        "* Mean of each row and column\n",
        "* Standard deviation of each row and column\n",
        "* Mean of the entire matrix\n",
        "* Standard deviation of entire matrix"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gMdm2pw0GWjf",
        "colab_type": "code",
        "outputId": "a0066aff-26f1-4723-9b93-3da59cf6fb85",
        "cellView": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        }
      },
      "source": [
        "#@title Default title text\n",
        "# Mean and Standard deviation of each row and column \n",
        "a=X.mean(axis=1)\n",
        "b=X.mean(axis=0)\n",
        "c=X.std(axis=1)\n",
        "d=X.std(axis=0)\n",
        "a, b, c,d\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([0.56706085, 0.66447172, 0.57705944, 0.51762729, 0.62761197,\n",
              "        0.5328907 , 0.41643268, 0.69444672, 0.44423265, 0.33781717]),\n",
              " array([0.56044382, 0.46781457, 0.62009909, 0.64025127, 0.40121685]),\n",
              " array([0.09445299, 0.23322986, 0.29189733, 0.38052993, 0.30431633,\n",
              "        0.26338419, 0.25841437, 0.12727959, 0.23169975, 0.18537332]),\n",
              " array([0.24687647, 0.25752158, 0.22948615, 0.28054144, 0.26584905]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 80
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XTszhe1oQ22N",
        "colab_type": "code",
        "outputId": "35588265-f53f-4a99-d3fe-3c68df6424a1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "# Mean and Standard deviation of entire matrix X\n",
        "print(\"min(X) = {}\".format(np.min(X)))\n",
        "print(\"argmin(X) = {}\".format(np.argmin(X)))\n",
        "print(\"mean(X) = {}\".format(np.mean(X)))\n",
        "print(\"var(X) = {}\".format(np.var(X)))\n",
        "print(\"std(X) = {}\".format(np.std(X)))\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "min(X) = 0.018789800436355142\n",
            "argmin(X) = 34\n",
            "mean(X) = 0.5379651182755409\n",
            "var(X) = 0.0741286783312718\n",
            "std(X) = 0.27226582292177587\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7dw7W8HOGXKA",
        "colab_type": "text"
      },
      "source": [
        "Let $Y$ denote a square matrix of size 10 with random values. Print the following:\n",
        "* Determinant\n",
        "* Rank of the matrix\n",
        "* Diagonal Elements\n",
        "* Trace\n",
        "* Eigen values\n",
        "* Matrices obtained after Singular Value Decomposition\n",
        "* Inverse if exists, otherwise Pseudo-Inverse\n",
        "* Multiplication $Y$ with $X$\n",
        "* Element-wise multiplication of $Y$ and its inverse(or pseudo-inverse)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Tswbn9hgL7yi",
        "colab_type": "code",
        "outputId": "934abd04-70a8-4e34-edd1-8e8daea5b723",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "np.random.seed(3)\n",
        "Y = np.random.rand(10,10)\n",
        "Y\n",
        "\n",
        "# compute the determinant, rank, diagonal elements and trace of Y\n",
        "det = np.linalg.det(Y)\n",
        "print(\"determinant(Y)= {}\".format(det))\n",
        "rank = np.linalg.matrix_rank(Y)\n",
        "print(\"rank(Y)= {}\".format(rank))\n",
        "diag_Y = np.diag(Y)\n",
        "print('diag_Y = {}'.format(diag_Y))\n",
        "trace = np.trace(Y)\n",
        "print(\"trace(Y)= {}\".format(trace))\n",
        "\n",
        "# eigen values and the eigen vectors of matrix Y\n",
        "eigen_val,eigen_vec = np.linalg.eig(Y)\n",
        "print(\"the eigen values of Y:\\n{}\".format(eigen_val))\n",
        "print(\"the the right eigen vectors of Y:\\n{}\".format(eigen_vec))\n",
        "\n",
        "# singular value decomposition on matrix Y\n",
        "u,s,vh = np.linalg.svd(Y)\n",
        "print(\"U of Y is :\\n{}\".format(u))\n",
        "print(\"V of Y is :\\n{}\".format(vh))\n",
        "print(\"singular values of Y are :\\n{}\".format(s))\n",
        "\n",
        "#  the (multiplicative) inverse of matrix Y\n",
        "print(\"the inverse of Y is:\")\n",
        "Inv_Y = np.linalg.inv(Y)\n",
        "print(Inv_Y)\n",
        "\n",
        "# the (Moore-Penrose) pseudo-inverse of Y\n",
        "print(\"the pseudo-inverse of Y is:\")\n",
        "Ps_InvY = np.linalg.pinv(Y)\n",
        "print(Ps_InvY)\n",
        "\n",
        "# Multiplication  Y  with  X\n",
        "Mult_YX = Y.dot(X)\n",
        "print(\"the matrix multiplication is:\")\n",
        "print(Mult_YX)\n",
        "\n",
        "# Element-wise multiplication of  Y  and its inverse\n",
        "elem_Y= np.multiply(Y, Inv_Y)\n",
        "print(\"the elementwise matrix multiplication is:\")\n",
        "print(elem_Y)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "determinant(Y)= -0.012807808169095483\n",
            "rank(Y)= 10\n",
            "diag_Y = [0.5507979  0.45683322 0.44045372 0.84575087 0.4576864  0.36217621\n",
            " 0.06152893 0.19897603 0.92672568 0.19638058]\n",
            "trace(Y)= 4.497309545724899\n",
            "the eigen values of Y:\n",
            "[ 4.797525  +0.j          0.72411408+0.52238181j  0.72411408-0.52238181j\n",
            " -0.48250062+0.55413671j -0.48250062-0.55413671j -0.6909002 +0.j\n",
            " -0.25905659+0.32357377j -0.25905659-0.32357377j  0.2127855 +0.08352477j\n",
            "  0.2127855 -0.08352477j]\n",
            "the the right eigen vectors of Y:\n",
            "[[ 0.29593906+0.j          0.14213977+0.19798456j  0.14213977-0.19798456j\n",
            "  -0.37236549+0.00325385j -0.37236549-0.00325385j -0.1096481 +0.j\n",
            "  -0.0132423 +0.12273111j -0.0132423 -0.12273111j -0.56228934-0.10973258j\n",
            "  -0.56228934+0.10973258j]\n",
            " [ 0.25059285+0.j          0.01404552+0.1967944j   0.01404552-0.1967944j\n",
            "  -0.16781094-0.17307308j -0.16781094+0.17307308j -0.29711444+0.j\n",
            "  -0.04108937-0.4113554j  -0.04108937+0.4113554j   0.61892544+0.j\n",
            "   0.61892544-0.j        ]\n",
            " [ 0.31416894+0.j         -0.24186998+0.15655466j -0.24186998-0.15655466j\n",
            "  -0.16993115+0.15284371j -0.16993115-0.15284371j  0.36362726+0.j\n",
            "  -0.10206063+0.15541211j -0.10206063-0.15541211j  0.16701388+0.18450241j\n",
            "   0.16701388-0.18450241j]\n",
            " [ 0.36027404+0.j          0.52448941+0.j          0.52448941-0.j\n",
            "   0.48969059+0.j          0.48969059-0.j          0.17074825+0.j\n",
            "   0.14078898+0.01851681j  0.14078898-0.01851681j -0.13278372+0.03975259j\n",
            "  -0.13278372-0.03975259j]\n",
            " [ 0.27990836+0.j         -0.13624801+0.01805996j -0.13624801-0.01805996j\n",
            "  -0.0731246 -0.10412128j -0.0731246 +0.10412128j  0.13537705+0.j\n",
            "  -0.29263074+0.368267j   -0.29263074-0.368267j   -0.07942445-0.1381196j\n",
            "  -0.07942445+0.1381196j ]\n",
            " [ 0.30697292+0.j         -0.2288709 -0.09164898j -0.2288709 +0.09164898j\n",
            "   0.34166486-0.10037728j  0.34166486+0.10037728j  0.38961338+0.j\n",
            "   0.1575938 -0.27237341j  0.1575938 +0.27237341j -0.05056956+0.01833742j\n",
            "  -0.05056956-0.01833742j]\n",
            " [ 0.28526996+0.j         -0.07276121-0.22120787j -0.07276121+0.22120787j\n",
            "  -0.09920762+0.30369397j -0.09920762-0.30369397j -0.38942645+0.j\n",
            "  -0.35795075-0.21303717j -0.35795075+0.21303717j  0.25824685-0.05397791j\n",
            "   0.25824685+0.05397791j]\n",
            " [ 0.23358056+0.j          0.33195752+0.22875065j  0.33195752-0.22875065j\n",
            "   0.22899202+0.29805206j  0.22899202-0.29805206j -0.15526644+0.j\n",
            "   0.47450761+0.j          0.47450761-0.j          0.01343252-0.05360821j\n",
            "   0.01343252+0.05360821j]\n",
            " [ 0.39548419+0.j         -0.14569343-0.47441452j -0.14569343+0.47441452j\n",
            "  -0.29937425-0.1334132j  -0.29937425+0.1334132j   0.26931546+0.j\n",
            "   0.07126882+0.08476271j  0.07126882-0.08476271j -0.02419704-0.00279054j\n",
            "  -0.02419704+0.00279054j]\n",
            " [ 0.3952166 +0.j         -0.02644966-0.01254236j -0.02644966+0.01254236j\n",
            "   0.09200666-0.09461051j  0.09200666+0.09461051j -0.5656002 +0.j\n",
            "   0.04736886+0.16022229j  0.04736886-0.16022229j -0.31202472+0.09318458j\n",
            "  -0.31202472-0.09318458j]]\n",
            "U of Y is :\n",
            "[[-0.31776408 -0.02455508 -0.60644878 -0.17883359 -0.12672161  0.14873878\n",
            "  -0.17823942 -0.52859453 -0.02295855 -0.38570883]\n",
            " [-0.26118514 -0.10864541 -0.24911354  0.26547359  0.52168399 -0.25773901\n",
            "  -0.46995326  0.21752636 -0.39285046  0.16234491]\n",
            " [-0.31347907 -0.34483471 -0.25292297  0.1214296   0.1486964   0.33436315\n",
            "   0.54080229  0.48017168  0.05660692 -0.20966421]\n",
            " [-0.35815379  0.59490017  0.30255161  0.15850614 -0.11046295  0.3051409\n",
            "   0.07395537  0.03044889 -0.50561658 -0.18384856]\n",
            " [-0.28385845 -0.18085696 -0.1583078   0.10535533 -0.46807835 -0.08377643\n",
            "   0.24075452 -0.16170764 -0.24786952  0.69201648]\n",
            " [-0.28871348 -0.27577124  0.40271105  0.60433658  0.11931679 -0.04899205\n",
            "   0.02593316 -0.44875145  0.27874747 -0.12964796]\n",
            " [-0.27897316  0.00398904  0.20819753 -0.52536617  0.41116881 -0.41991923\n",
            "   0.42687225 -0.24145621 -0.12958507 -0.00984813]\n",
            " [-0.24788529  0.48136836 -0.15792433 -0.02303902  0.3246308   0.25755952\n",
            "  -0.01429533 -0.03088365  0.56052488  0.44079262]\n",
            " [-0.37505167 -0.36728578  0.39799373 -0.45186801 -0.10830044  0.34456765\n",
            "  -0.4447402   0.14147957  0.0716725   0.09192695]\n",
            " [-0.40049601  0.19846099 -0.02705464  0.02500837 -0.39745062 -0.57941613\n",
            "  -0.10288216  0.3673956   0.33321483 -0.22039139]]\n",
            "V of Y is :\n",
            "[[-0.28816735 -0.35560525 -0.33294235 -0.33250662 -0.36658188 -0.3625847\n",
            "  -0.26573249 -0.23278667 -0.30457183 -0.29270444]\n",
            " [ 0.53693497  0.11306854  0.39562078  0.25099719 -0.07369559 -0.37753546\n",
            "  -0.08584363  0.00333609 -0.2399022  -0.51623983]\n",
            " [-0.084609   -0.22589744 -0.00306935  0.1954239  -0.327784   -0.49318928\n",
            "   0.42323124  0.18588504  0.58200169  0.02301787]\n",
            " [ 0.01388163 -0.2631197   0.42190391 -0.53612946  0.01058633 -0.04415909\n",
            "   0.29385139  0.49501812 -0.32731018  0.15669071]\n",
            " [-0.27340804  0.28220631  0.28945859 -0.1626885   0.14790418 -0.35915036\n",
            "  -0.64971879  0.23854611  0.29589227  0.1337842 ]\n",
            " [ 0.10830593  0.27974551 -0.20571161  0.10308827  0.10096026 -0.5325142\n",
            "   0.15994871 -0.16150892 -0.3941055   0.59692177]\n",
            " [ 0.44882085  0.34972045 -0.01773924 -0.50737391 -0.52251393  0.11970007\n",
            "  -0.02807841 -0.20137782  0.25705553  0.15409283]\n",
            " [-0.35599817 -0.05022624  0.63427946  0.20935183 -0.34847081  0.11510691\n",
            "   0.03182222 -0.47748403 -0.1161671   0.21777064]\n",
            " [ 0.18417681 -0.32168889  0.15954963 -0.32397524  0.5548368  -0.1807982\n",
            "   0.08626619 -0.55063636  0.28439362 -0.01119242]\n",
            " [-0.41560913  0.59522266  0.02089304 -0.23979844  0.13515565 -0.0893732\n",
            "   0.44674689 -0.10709455 -0.02239562 -0.42098815]]\n",
            "singular values of Y are :\n",
            "[4.89636645 1.42832104 1.17173389 0.94068764 0.76892251 0.62457278\n",
            " 0.52105948 0.28969576 0.24512275 0.09350223]\n",
            "the inverse of Y is:\n",
            "[[ 2.31470983 -1.92264991  0.7642126   0.78096977 -2.74248585  1.20175092\n",
            "   0.38693174 -1.37664514 -0.96484143  0.83123246]\n",
            " [-2.24504111  1.25605742 -0.91466223 -0.39587642  4.71823627 -1.32162185\n",
            "   0.52594984  2.39368168  0.33051878 -2.33540101]\n",
            " [-1.41290916  0.66149939  0.94968095 -0.18869248 -0.50069581 -0.55664939\n",
            "  -0.55275157  0.57384943 -0.04209635  1.11025544]\n",
            " [ 0.88051129  0.37055438  0.15632501  1.25248223 -1.81219563 -0.7249179\n",
            "  -0.19613524 -1.81766381  0.56943994  0.52226388]\n",
            " [ 0.39743656 -0.28842728 -1.09880632 -1.57965965  0.36480771  0.90235521\n",
            "  -0.47743451  2.09911148  0.53638288 -0.04562024]\n",
            " [ 0.36068175  0.22958502  0.33426258  0.10367281 -0.06700744 -0.37158555\n",
            "   0.22972702 -1.26286862 -0.45133033  0.75430018]\n",
            " [-2.01045364  0.19347423 -1.01393804 -0.74303568  3.56449935 -0.31892146\n",
            "  -0.67116163  2.01265699  0.72873355 -0.69454601]\n",
            " [ 1.18043988  0.86047396 -0.88991494  1.30425635 -0.14247318  0.69661973\n",
            "   0.5413572  -1.69774697 -0.60797727 -1.00698216]\n",
            " [-0.1679456  -0.63197036 -0.0540802  -0.73587818 -0.46423184  0.67805628\n",
            "   0.88551393  0.37662528 -0.03416891  0.42341327]\n",
            " [ 1.3938872  -0.74982353  1.96636643  1.00676681 -3.21953806  0.44078124\n",
            "  -0.40298654 -1.90114336 -0.04414834  0.55576763]]\n",
            "the pseudo-inverse of Y is:\n",
            "[[ 2.31470983 -1.92264991  0.7642126   0.78096977 -2.74248585  1.20175092\n",
            "   0.38693174 -1.37664514 -0.96484143  0.83123246]\n",
            " [-2.24504111  1.25605742 -0.91466223 -0.39587642  4.71823627 -1.32162185\n",
            "   0.52594984  2.39368168  0.33051878 -2.33540101]\n",
            " [-1.41290916  0.66149939  0.94968095 -0.18869248 -0.50069581 -0.55664939\n",
            "  -0.55275157  0.57384943 -0.04209635  1.11025544]\n",
            " [ 0.88051129  0.37055438  0.15632501  1.25248223 -1.81219563 -0.7249179\n",
            "  -0.19613524 -1.81766381  0.56943994  0.52226388]\n",
            " [ 0.39743656 -0.28842728 -1.09880632 -1.57965965  0.36480771  0.90235521\n",
            "  -0.47743451  2.09911148  0.53638288 -0.04562024]\n",
            " [ 0.36068175  0.22958502  0.33426258  0.10367281 -0.06700744 -0.37158555\n",
            "   0.22972702 -1.26286862 -0.45133033  0.75430018]\n",
            " [-2.01045364  0.19347423 -1.01393804 -0.74303568  3.56449935 -0.31892146\n",
            "  -0.67116163  2.01265699  0.72873355 -0.69454601]\n",
            " [ 1.18043988  0.86047396 -0.88991494  1.30425635 -0.14247318  0.69661973\n",
            "   0.5413572  -1.69774697 -0.60797727 -1.00698216]\n",
            " [-0.1679456  -0.63197036 -0.0540802  -0.73587818 -0.46423184  0.67805628\n",
            "   0.88551393  0.37662528 -0.03416891  0.42341327]\n",
            " [ 1.3938872  -0.74982353  1.96636643  1.00676681 -3.21953806  0.44078124\n",
            "  -0.40298654 -1.90114336 -0.04414834  0.55576763]]\n",
            "the matrix multiplication is:\n",
            "[[2.95726101 2.04939653 3.09073485 3.22311637 1.78554985]\n",
            " [2.61266989 1.75663954 2.48635951 2.79783984 1.50654432]\n",
            " [2.98361778 2.02894044 2.82637865 2.88685728 1.69799548]\n",
            " [2.98565892 2.85485651 3.58995669 4.0073463  2.2697569 ]\n",
            " [2.49815821 1.97791033 2.77809758 2.71690515 1.59098767]\n",
            " [2.72146909 2.39905911 2.58780909 2.78212857 1.71792628]\n",
            " [2.22935358 1.74438251 2.94718357 2.48955906 2.05838199]\n",
            " [2.30476788 1.92350098 2.41698824 2.81379687 1.38016019]\n",
            " [2.91925254 2.36604123 3.53647969 3.30424184 2.52990887]\n",
            " [3.39559098 2.84629279 4.05845051 4.01068273 2.35816262]]\n",
            "the elementwise matrix multiplication is:\n",
            "[[ 1.27493732 -1.36152035  0.22231307  0.39894092 -2.44889439  1.07712104\n",
            "   0.04859294 -0.2852999  -0.04965769  0.36641545]\n",
            " [-0.06707332  0.57380876 -0.59374754 -0.11024655  3.19073041 -0.78089721\n",
            "   0.01261327  1.33771879  0.0856878  -0.96942775]\n",
            " [-0.40059519  0.45851031  0.4182905  -0.02959976 -0.27270348 -0.43436174\n",
            "  -0.16934292  0.12737041 -0.01633217  1.03962504]\n",
            " [ 0.85937499  0.24915472  0.14113555  1.05928794 -0.68499915 -0.06684976\n",
            "  -0.12815691 -1.01396696  0.20588942  0.11753784]\n",
            " [ 0.16156588 -0.13525516 -0.29583776 -0.46093327  0.16696753  0.77650726\n",
            "  -0.27989737  0.59507263  0.14910237 -0.02073997]\n",
            " [ 0.07408776  0.04623354  0.17182269  0.00904331 -0.03240383 -0.13457945\n",
            "   0.16257474 -0.94304237 -0.3119112   0.51984891]\n",
            " [-0.75110573  0.12926687 -0.34458549 -0.42560628  1.1613394  -0.14196631\n",
            "  -0.04129586  0.48842239  0.70803941 -0.16015134]\n",
            " [ 0.81624763  0.5597184  -0.64424426  0.61963734 -0.08500859  0.04665222\n",
            "   0.03928204 -0.33781095 -0.09232803 -0.10080329]\n",
            " [-0.02171434 -0.34965513 -0.01015706 -0.70063053 -0.31642589  0.36684179\n",
            "   0.62621827  0.09938639 -0.03166521  0.35532547]\n",
            " [ 1.01240745 -0.36009522  1.65588343  0.74979192 -2.12594439  0.40286315\n",
            "  -0.25535869 -0.69570551 -0.02440717  0.10914197]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LA-m4UYkMPTe",
        "colab_type": "text"
      },
      "source": [
        "## Part - 2\n",
        "---\n",
        "In this part, you will be working with the library ```pandas```. Import this library with an alias name ```pd```."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i8z7TpnZSIms",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Initial imports\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "import seaborn as sns\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2v-HkHnyuQ3X",
        "colab_type": "text"
      },
      "source": [
        "Download dataset from: http://biostat.mc.vanderbilt.edu/wiki/pub/Main/DataSets/titanic3.csv\n",
        "Read the data and display the first 5 rows"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LinX5ywNTUIm",
        "colab_type": "code",
        "outputId": "20e3a413-eeef-4cd3-c36f-585b68583bb8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        }
      },
      "source": [
        "#Download dataset from: http://biostat.mc.vanderbilt.edu/wiki/pub/Main/DataSets/titanic3.csv\n",
        "\n",
        "file_url = \"http://biostat.mc.vanderbilt.edu/wiki/pub/Main/DataSets/titanic3.csv\"\n",
        "file_url\n",
        "\n",
        "Data = pd.read_csv(file_url)\n",
        "Data.head(5)\n"
      ],
      "execution_count": 190,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>pclass</th>\n",
              "      <th>survived</th>\n",
              "      <th>name</th>\n",
              "      <th>sex</th>\n",
              "      <th>age</th>\n",
              "      <th>sibsp</th>\n",
              "      <th>parch</th>\n",
              "      <th>ticket</th>\n",
              "      <th>fare</th>\n",
              "      <th>cabin</th>\n",
              "      <th>embarked</th>\n",
              "      <th>boat</th>\n",
              "      <th>body</th>\n",
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              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>Allen, Miss. Elisabeth Walton</td>\n",
              "      <td>female</td>\n",
              "      <td>29.00</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>24160</td>\n",
              "      <td>211.3375</td>\n",
              "      <td>B5</td>\n",
              "      <td>S</td>\n",
              "      <td>2</td>\n",
              "      <td>NaN</td>\n",
              "      <td>St Louis, MO</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>Allison, Master. Hudson Trevor</td>\n",
              "      <td>male</td>\n",
              "      <td>0.92</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>113781</td>\n",
              "      <td>151.5500</td>\n",
              "      <td>C22 C26</td>\n",
              "      <td>S</td>\n",
              "      <td>11</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Montreal, PQ / Chesterville, ON</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>Allison, Miss. Helen Loraine</td>\n",
              "      <td>female</td>\n",
              "      <td>2.00</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>113781</td>\n",
              "      <td>151.5500</td>\n",
              "      <td>C22 C26</td>\n",
              "      <td>S</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Montreal, PQ / Chesterville, ON</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>Allison, Mr. Hudson Joshua Creighton</td>\n",
              "      <td>male</td>\n",
              "      <td>30.00</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>113781</td>\n",
              "      <td>151.5500</td>\n",
              "      <td>C22 C26</td>\n",
              "      <td>S</td>\n",
              "      <td>NaN</td>\n",
              "      <td>135.0</td>\n",
              "      <td>Montreal, PQ / Chesterville, ON</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>Allison, Mrs. Hudson J C (Bessie Waldo Daniels)</td>\n",
              "      <td>female</td>\n",
              "      <td>25.00</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>113781</td>\n",
              "      <td>151.5500</td>\n",
              "      <td>C22 C26</td>\n",
              "      <td>S</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Montreal, PQ / Chesterville, ON</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   pclass  survived  ...   body                        home.dest\n",
              "0       1         1  ...    NaN                     St Louis, MO\n",
              "1       1         1  ...    NaN  Montreal, PQ / Chesterville, ON\n",
              "2       1         0  ...    NaN  Montreal, PQ / Chesterville, ON\n",
              "3       1         0  ...  135.0  Montreal, PQ / Chesterville, ON\n",
              "4       1         0  ...    NaN  Montreal, PQ / Chesterville, ON\n",
              "\n",
              "[5 rows x 14 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 190
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vTk1-mF5WYFN",
        "colab_type": "text"
      },
      "source": [
        "### Preprocessing of the Dataset"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kx9UrI9WWt17",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "**1. Convert the categorical values of columns 'sex', 'embarked', 'pclass' into dummy values and add them into titanic_data_new DataFrame**\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AwDh9njbZ0QU",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "outputId": "0c020a1e-13c8-4de7-8530-fac53da1d8ab"
      },
      "source": [
        "# sex_d=pd.get_dummies(Data['sex'])\n",
        "# sex_d\n",
        "# emb_d=pd.get_dummies(Data['embarked'])\n",
        "# emb_d\n",
        "# pclass_d=pd.get_dummies(Data['pclass'])\n",
        "# pclass_d\n",
        "############################\n",
        "Data['Sex_male'] = Data.sex.map({'female':0, 'male':1})\n",
        "pd.get_dummies(Data.sex)\n",
        "pd.get_dummies(Data.sex, prefix='sex').iloc[:, 1:]\n",
        "sex_d=pd.get_dummies(Data.sex, prefix='sex').loc[:, 'Sex_male':]\n",
        "sex_d\n",
        "Data.embarked.value_counts()\n",
        "pd.get_dummies(Data.embarked, prefix='Embarked').iloc[:, 1:]\n",
        "embarked_d = pd.get_dummies(Data.embarked, prefix='Embarked').iloc[:, 1:]\n",
        "embarked_d\n",
        "Data.pclass.value_counts()\n",
        "pd.get_dummies(Data.pclass, prefix='pclass').iloc[:, 1:]\n",
        "pclass_d = pd.get_dummies(Data.pclass, prefix='pclass').iloc[:, 1:]\n",
        "pclass_d\n",
        "pd.concat([Data, embarked_d], axis=1)\n",
        "titanic_data_new= pd.get_dummies(Data, columns=['sex', 'embarked', 'pclass'], drop_first=True)\n",
        "titanic_data_new"
      ],
      "execution_count": 195,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>survived</th>\n",
              "      <th>name</th>\n",
              "      <th>age</th>\n",
              "      <th>sibsp</th>\n",
              "      <th>parch</th>\n",
              "      <th>ticket</th>\n",
              "      <th>fare</th>\n",
              "      <th>cabin</th>\n",
              "      <th>boat</th>\n",
              "      <th>body</th>\n",
              "      <th>home.dest</th>\n",
              "      <th>Sex_male</th>\n",
              "      <th>sex_male</th>\n",
              "      <th>embarked_Q</th>\n",
              "      <th>embarked_S</th>\n",
              "      <th>pclass_2</th>\n",
              "      <th>pclass_3</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>Allen, Miss. Elisabeth Walton</td>\n",
              "      <td>29.00</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>24160</td>\n",
              "      <td>211.3375</td>\n",
              "      <td>B5</td>\n",
              "      <td>2</td>\n",
              "      <td>NaN</td>\n",
              "      <td>St Louis, MO</td>\n",
              "      <td>0</td>\n",
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              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>Allison, Master. Hudson Trevor</td>\n",
              "      <td>0.92</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>113781</td>\n",
              "      <td>151.5500</td>\n",
              "      <td>C22 C26</td>\n",
              "      <td>11</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Montreal, PQ / Chesterville, ON</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0</td>\n",
              "      <td>Allison, Miss. Helen Loraine</td>\n",
              "      <td>2.00</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>113781</td>\n",
              "      <td>151.5500</td>\n",
              "      <td>C22 C26</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Montreal, PQ / Chesterville, ON</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
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              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0</td>\n",
              "      <td>Allison, Mr. Hudson Joshua Creighton</td>\n",
              "      <td>30.00</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>113781</td>\n",
              "      <td>151.5500</td>\n",
              "      <td>C22 C26</td>\n",
              "      <td>NaN</td>\n",
              "      <td>135.0</td>\n",
              "      <td>Montreal, PQ / Chesterville, ON</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0</td>\n",
              "      <td>Allison, Mrs. Hudson J C (Bessie Waldo Daniels)</td>\n",
              "      <td>25.00</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>113781</td>\n",
              "      <td>151.5500</td>\n",
              "      <td>C22 C26</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Montreal, PQ / Chesterville, ON</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1304</th>\n",
              "      <td>0</td>\n",
              "      <td>Zabour, Miss. Hileni</td>\n",
              "      <td>14.50</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2665</td>\n",
              "      <td>14.4542</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>328.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1305</th>\n",
              "      <td>0</td>\n",
              "      <td>Zabour, Miss. Thamine</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2665</td>\n",
              "      <td>14.4542</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1306</th>\n",
              "      <td>0</td>\n",
              "      <td>Zakarian, Mr. Mapriededer</td>\n",
              "      <td>26.50</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2656</td>\n",
              "      <td>7.2250</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>304.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1307</th>\n",
              "      <td>0</td>\n",
              "      <td>Zakarian, Mr. Ortin</td>\n",
              "      <td>27.00</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2670</td>\n",
              "      <td>7.2250</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1308</th>\n",
              "      <td>0</td>\n",
              "      <td>Zimmerman, Mr. Leo</td>\n",
              "      <td>29.00</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>315082</td>\n",
              "      <td>7.8750</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>1309 rows × 17 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "      survived  ... pclass_3\n",
              "0            1  ...        0\n",
              "1            1  ...        0\n",
              "2            0  ...        0\n",
              "3            0  ...        0\n",
              "4            0  ...        0\n",
              "...        ...  ...      ...\n",
              "1304         0  ...        1\n",
              "1305         0  ...        1\n",
              "1306         0  ...        1\n",
              "1307         0  ...        1\n",
              "1308         0  ...        1\n",
              "\n",
              "[1309 rows x 17 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 195
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z9bxOfzDbY-n",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "**2. Fill the missing data in Age and Fare columns with the mean value of the respected column then add these columns to titanic_data_new**\n",
        "\n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DNx7Pr0ehhAs",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 521
        },
        "outputId": "18f08723-b86e-4b19-9ae6-1dd970bf0022"
      },
      "source": [
        "m_a= titanic_data_new['age'].mean()\n",
        "m_f= titanic_data_new['fare'].mean()\n",
        "new_age= titanic_data_new['age'].fillna(m_a)\n",
        "new_fare= titanic_data_new['fare'].fillna(m_f)\n",
        "titanic_data_new['new_age']= new_age\n",
        "titanic_data_new['new_fare']= new_fare\n",
        "titanic_data_new"
      ],
      "execution_count": 304,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
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              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>survived</th>\n",
              "      <th>name</th>\n",
              "      <th>age</th>\n",
              "      <th>sibsp</th>\n",
              "      <th>parch</th>\n",
              "      <th>ticket</th>\n",
              "      <th>fare</th>\n",
              "      <th>cabin</th>\n",
              "      <th>boat</th>\n",
              "      <th>body</th>\n",
              "      <th>home.dest</th>\n",
              "      <th>Sex_male</th>\n",
              "      <th>sex_male</th>\n",
              "      <th>embarked_Q</th>\n",
              "      <th>embarked_S</th>\n",
              "      <th>pclass_2</th>\n",
              "      <th>pclass_3</th>\n",
              "      <th>new_age</th>\n",
              "      <th>new_fare</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>Allen, Miss. Elisabeth Walton</td>\n",
              "      <td>29.00</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>24160</td>\n",
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              "      <td>B5</td>\n",
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              "      <td>NaN</td>\n",
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              "      <td>29.000000</td>\n",
              "      <td>211.3375</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>Allison, Master. Hudson Trevor</td>\n",
              "      <td>0.92</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>113781</td>\n",
              "      <td>151.5500</td>\n",
              "      <td>C22 C26</td>\n",
              "      <td>11</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Montreal, PQ / Chesterville, ON</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0.920000</td>\n",
              "      <td>151.5500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0</td>\n",
              "      <td>Allison, Miss. Helen Loraine</td>\n",
              "      <td>2.00</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>113781</td>\n",
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              "      <td>C22 C26</td>\n",
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              "      <td>NaN</td>\n",
              "      <td>Montreal, PQ / Chesterville, ON</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2.000000</td>\n",
              "      <td>151.5500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0</td>\n",
              "      <td>Allison, Mr. Hudson Joshua Creighton</td>\n",
              "      <td>30.00</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>113781</td>\n",
              "      <td>151.5500</td>\n",
              "      <td>C22 C26</td>\n",
              "      <td>NaN</td>\n",
              "      <td>135.0</td>\n",
              "      <td>Montreal, PQ / Chesterville, ON</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>30.000000</td>\n",
              "      <td>151.5500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0</td>\n",
              "      <td>Allison, Mrs. Hudson J C (Bessie Waldo Daniels)</td>\n",
              "      <td>25.00</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>113781</td>\n",
              "      <td>151.5500</td>\n",
              "      <td>C22 C26</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>Montreal, PQ / Chesterville, ON</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>25.000000</td>\n",
              "      <td>151.5500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1304</th>\n",
              "      <td>0</td>\n",
              "      <td>Zabour, Miss. Hileni</td>\n",
              "      <td>14.50</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2665</td>\n",
              "      <td>14.4542</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>328.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>14.500000</td>\n",
              "      <td>14.4542</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1305</th>\n",
              "      <td>0</td>\n",
              "      <td>Zabour, Miss. Thamine</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2665</td>\n",
              "      <td>14.4542</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>29.881138</td>\n",
              "      <td>14.4542</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1306</th>\n",
              "      <td>0</td>\n",
              "      <td>Zakarian, Mr. Mapriededer</td>\n",
              "      <td>26.50</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2656</td>\n",
              "      <td>7.2250</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>304.0</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>26.500000</td>\n",
              "      <td>7.2250</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1307</th>\n",
              "      <td>0</td>\n",
              "      <td>Zakarian, Mr. Ortin</td>\n",
              "      <td>27.00</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>2670</td>\n",
              "      <td>7.2250</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>27.000000</td>\n",
              "      <td>7.2250</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1308</th>\n",
              "      <td>0</td>\n",
              "      <td>Zimmerman, Mr. Leo</td>\n",
              "      <td>29.00</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>315082</td>\n",
              "      <td>7.8750</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>29.000000</td>\n",
              "      <td>7.8750</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>1309 rows × 19 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "      survived  ...  new_fare\n",
              "0            1  ...  211.3375\n",
              "1            1  ...  151.5500\n",
              "2            0  ...  151.5500\n",
              "3            0  ...  151.5500\n",
              "4            0  ...  151.5500\n",
              "...        ...  ...       ...\n",
              "1304         0  ...   14.4542\n",
              "1305         0  ...   14.4542\n",
              "1306         0  ...    7.2250\n",
              "1307         0  ...    7.2250\n",
              "1308         0  ...    7.8750\n",
              "\n",
              "[1309 rows x 19 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 304
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SlRzKfhxkd1M",
        "colab_type": "text"
      },
      "source": [
        "###Normalization\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "\n",
        "1. Normalize the columns which have numerical data\n",
        "\n",
        "\n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y3hpu92TlM38",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "import seaborn as sns\n",
        "import pandas as pd\n",
        "from sklearn.preprocessing import Normalizer\n",
        "a=titanic_data_new.select_dtypes(include=['float64'])\n",
        "b=a.keys()\n",
        "for keys in b:\n",
        "  titanic_data_new[keys]=(a[keys]-a[keys].mean())/a[keys].std()\n",
        "  print(keys)\n",
        "  print(titanic_data_new)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wB9-5x83mFAO",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "---\n",
        "2. Drop the original age, fare columns\n",
        "3. Append the normalized columns to the titanic_data_new DataFrame.\n",
        "\n",
        "\n",
        "\n",
        "---\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Kb00kM0onQJy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "titanic_data_new_1=titanic_data_new.drop(columns=['age', 'fare'])\n",
        "titanic_data_new=titanic_data_new.append(titanic_data_new_1, ignore_index = True)\n",
        "titanic_data_new"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uLxN3PozntKe",
        "colab_type": "text"
      },
      "source": [
        "###Plotting\n",
        "1. plot the age against the ID(continuous)\n",
        "2. plot the fare against the ID(scatter)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LdSfNEKYn_RO",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 558
        },
        "outputId": "b9ba1521-f497-473a-c54f-abb75eaa9997"
      },
      "source": [
        "age= titanic_data_new['new_age']\n",
        "fare=titanic_data_new['new_fare']\n",
        "#indx=titanic_data_new['index']\n",
        "X=titanic_data_new.reset_index().plot(x='index', y='new_age')\n",
        "X.set_xlim(0,1309)\n",
        "Y=titanic_data_new.reset_index().plot.scatter(x='index', y='new_fare')\n",
        "Y.set_xlim(0,1309)\n"
      ],
      "execution_count": 393,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.0, 1309.0)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 393
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TWhZcKvfvW2B",
        "colab_type": "text"
      },
      "source": [
        "## Part - 3\n",
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8bY4H9DszQ2S",
        "colab_type": "text"
      },
      "source": [
        "In this part, you will work with the library ```matplotlib```. Import the ```pyplot``` from ```matplotlib``` with an alias name ```plt```."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hPN6qctRzknT",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Initial imports\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fQ6KX_Aezlub",
        "colab_type": "text"
      },
      "source": [
        "Plot the sine function with domain in $[-3\\pi,3\\pi]$. Label the axes appropriately. Add title $\\sin(x)$. Use latex formatting while adding the title. Set the plot size to (10,10)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0tA3J5mA1cQ0",
        "colab_type": "code",
        "outputId": "00678aa4-fa98-41e4-ca18-84aec27a5311",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "x= np.linspace(-3*np.pi,3*np.pi,300)\n",
        "y= np.divide(np.sin(x),x)\n",
        "plt.title(r'$\\alpha$')\n",
        "plt.plot(x,y)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Vn5/YxwU0BNQw0BBQHmujY659bx4U7jInPZbCqqPUNLVaXYryMhoCymNtKKklIjiAiSOjrC5l2HUd7egiM8rZNASUx9pYWsfM1BH4+4nVpQy7qSnRBAX46UVjyuk0BJRHqj/Wzt6KRnLSvHtQuEtwgD/TU6L1SEA5nYaA8kib9tdhjH3hFV+Rkx7LjvJ6jrXpIjPKeTQElEfaWFKHv58ww4sWkelPTloMHTbD1jJdZEY5j4aA8kh5pbVkj4oiPNgp0195hK6zoPL0VFHlRBoCyuO0d9rYcuCIT3UFgX2RmazECB0XUE6lIaA8zs6DDbS023xmULi7nPRYNpbWYdNFZpSTaAgoj9PVHeJrRwJgHxdobOkgv7LR6lKUl9AQUB4nr6SOMbGhJEWFWF2Ky3XNlqrrDitn0RBQHsUYQ15pnU92BQGMiQ0lITKYjTo4rJxEQ0B5lP21zVQ3tfrEfEG9ERHmpMfokYByGg0B5VG6Pvy8eRGZ/sxOi6X8yDEO1esiM2roNASUR9lYWktUSABZiRFWl2KZ45PJ6dGAcgINAeVR8krqmJUWg58PTBrXl0mjoggN9D8+lbZSQ6EhoDzGkeY29lU2keOj4wFdAv39mJk6QheZUU6hIaA8xqb99m++OT48HtAlJy2G3YcaaGrtsLoU5eE0BJTHyCupI8BPmJ7iO5PG9SUnPRabgc37tUtIDY1TQkBEFonIXhEpEJG7TrDdN0XEiEiOM9pVviWvtI7Jo6MIDfK3uhTLzUwdgZ/o4LAauiGHgIj4A48Bi4FsYKmIZPeyXSRwB/DVUNtUvqetw8bWA0eY7aMXifUUGRLIxJFROjishswZRwK5QIExpsgY0wa8CFzcy3YPAL8HWpzQpvIxOw/W09ph88n5gvqSkx7Dpv11dHTarC5FeTBnhEAycKDb/TLHY8eJyCxgjDHm3RO9kIgsE5E8EcmrqqpyQmnKW3R94/X1M4O6y0mPpbmtkz2HdTI5dfKGfWBYRPyAPwL/2d+2xpgnjDE5xpichISE4S5NeZCuSeMSfXDSuL50BaKeKqqGwhkhUA6M6XY/xfFYl0hgCvCpiJQA84DlOjisBsrXJ43ry+gRoSSPCNVFZtSQOCMENgBZIpIhIkHAVcDyrieNMfXGmHhjTLoxJh1YBywxxuQ5oW3lA3x90rgTmZ0WQ15JLcboIjPq5Aw5BIwxHcBtwEpgN/CyMWaniNwvIkuG+vpKdZ0GqYPCXzcnPYaKhlbK6nQyOXVynLJKtzFmBbCix2P39rHtmc5oU/mOvNI6IoMDyEqMtLoUt9N1ymxeaS1jYsMsrkZ5Ir1iWLm9TaV1zEyLwd+HJ43ry4SRkUQGB+hFY+qkaQgot1Z/rJ38ykY9NbQP/n7CzLQYDQF10jQElFvbtL8OY/T6gBPJSYshv7KR+uZ2q0tRHkhDQLm1jSV1+PsJM1J10ri+5KTHYMz/zbKq1GBoCCi3lldaS/aoKMKCnHIOg1eaMWYE/n5CXqleNKYGT0NAua32ThtbDhzR6wP6ERYUwJTRUbr4vDopGgLKbe062EBLu04aNxCz02LZeuAIbR06mZwaHA0B5bbyjk8ap9NF9GdOegytHTZ2HKy3uhTlYTQElNvaWFpL8ohQRkbrpHH9me04WtqoXUJqkDQElFsyxpBXUqfjAQOUGBlCWlyYziiqBk1DQLmlsrpjVDa26njAIMxOi2FjaZ1OJqcGRUNAuaWuRWT0SGDg5qTHUnO0jeLqo1aXojyIhoByS3mltUQEBzBxZJTVpXiMrquqdX0BNRgaAsot5ZXUMTN1hE4aNwhjEyIYERZIno4LqEHQEFBup6Glnb0VjdoVNEh+fsLs1Bg9ElCDoiGg3I59cBNy0/X6gMHKSY+lqOooNU2tVpeiPISGgHI764trCfATZqbqkcBgdZ1NtVGPBtQAaQgot7O+uJZpKdGEBvlbXYrHmZocTZC/n4aAGjANAeVWjrV1sq3sCLkZcVaX4pFCAv2ZmhKtF42pAdMQUG5l84E62jsNczN0POBk5aTHsL28npb2TqtLUR5AQ0C5lfXFtYj831w4avBy0mJp7zRsK9PJ5FT/NASUW1lfbF9EJiok0OpSPNbs4xeNaZeQ6p+GgHIbbR02Nu2vI1e7goYkNjyIsQnhuvi8GhCnhICILBKRvSJSICJ39fL8nSKyS0S2ichHIpLmjHaVd7H3Y9t0PMAJ5qTHsrG0DptNJ5NTJzbkEBARf+AxYDGQDSwVkewem20Gcowx04BXgQeH2q7yPuuL7d0Xc/QisSGbnRZD/bF2CqqarC5FuTlnHAnkAgXGmCJjTBvwInBx9w2MMZ8YY5odd9cBKU5oV3mZ9cU1jEuMIC4i2OpSPF5XkGqXkOqPM0IgGTjQ7X6Z47G+3Ay819sTIrJMRPJEJK+qqsoJpSlP0WmzLyKj4wHOkRYXRnxEkE4mp/rl0oFhEbkGyAEe6u15Y8wTxpgcY0xOQkKCK0tTFtt9qIHG1g4dD3ASESEnLZb1GgKqH84IgXJgTLf7KY7H/o2ILATuAZYYY3R2K/VvvtLxAKebmxlLWd0xyuqa+99Y+SxnhMAGIEtEMkQkCLgKWN59AxGZCfwVewBUOqFN5WXWF9cwJjaU0SNCrS7Fa8wfa596Y21hjcWVKHc25BAwxnQAtwErgd3Ay8aYnSJyv4gscWz2EBABvCIiW0RkeR8vp3yQMYb1xbXkput8Qc40PjGS2PAg1hZpCKi+BTjjRYwxK4AVPR67t9vthc5oR3mnfZVN1DW3k5uhU0U4k5+fMC8zlnWFNRhjENFV2tTX6RXDynJfFlQDcMrYeIsr8T7zM+M4WN/C/lodF1C90xBQlvuy0D4eMCY2zOpSvI6OC6j+aAgoS3XaDOuKajglU48ChsPYhAgSIoN1XED1SUNAWWrnwXoaWjo4ZZwOCg8HEWFeZhxrHeMCSvWkIaAstabA/g21q9tCOd/8zDgqG1spqj5qdSnKDTnl7CBfUljVxKpdFWzeX0dBZRM1R9sACA8KICspgmnJ0SyaMopJoyL1bIwB+LKwmvFJESRGhlhditfqPi4wNiHC4mrcX1uHjc/yq1hbWMOm/XVUNbZypLmNiJAA4sKDmZIcRU56LOdOSiImPMjqcodMQ2AA2jttrNh+iL+vLmZ7uX21psyEcLISIzg1yv7hdaS5nfyKRj7Pr+KRjwsYnxTBD84ax4XTRuPvp2HQm9aOTjaU1HLVnFSrS/Fq6XFhJEXZxwWumaezuPflSHMbT31RzL/WH6C6qZXgAD9mjBnB3MxYokMDaW7tpKKxhQ92VfByXhmB/sK52UncsiCTmamee3qzhkA/PtlTyf3v7KK4+iiZCeH84qJszps8kuQ+rmytaWrlvR2HeW5tCXe8uIXHPynk95dPY8aYEa4t3ANs2X+ElnYbp2hX0LASEU4ZG8/n+VXYbAY//VLyb2w2wwsb9vM/K/dy5Fg7Z09I5Jr5aZwyNo7gAP9et999uIHXN5Xz+qYyVmw/zMJJidx9/iSPPNISdx0sysnJMXl5eZa1X93Uyt2vb2fVrgoyE8L56aKJnDspacB/QDab4d3th/jNit1UNLRw65lj+dHC8QT46zBMlz+uyud/P97H5nvPIzpUl5McTq9tLOM/X9nKO7efxpTkaKvLcRs1Ta388KUtrN5XTW5GLL9cMplJo6IG/PNHWzt4ek0xf/28iNYOG3eck8Wy0zMJtPDvXEQ2GmNyBrq9Hgn04pM9lfz41a00tHRw9+KJ3HhqBkEBg/ul+vkJF00fzRkTEnjg7V089kkh28sbeHTpTP3Ac1hbWM3U5GjdHy6wIMt+Cu7qfdUaAg5bDxxh2fN51DW38+tLp3B1buqgx/HCgwO47ewsrpwzhvuW7+ShlXv5aHcF/3v1LI+ZB0u/lnZjsxke/WgfNz27gfiIYN65/TS+e8bYQQdAd1EhgTx0xXR+e9lUviyo5rLH13Co/pgTq/ZMR1s72Lz/CPP1KmGXSIwKYeLISFbv03U6AD7Pr2Lp39YR6O/HG98/hW/PTRvSiRyJkSE8/u3ZPLp0JvkVTVzwyGq+2FftxIqHj4aAQ0t7J7e/sJk/rMrnkhnJvPmDUxmfFOm011+am8rzN8+loqGVq55Yx8Ejvh0E64tr6bAZTtXrA1xmQVY8eSV1NLd1WF2Kpd7fcZibn91AWlw4r996CpNHO+/I6KLpo1l+26kkRoZww9PreTnvQP8/ZDENAaCxpZ0bn97Au9sPcffiifzxyumEBH59QGio5o+N47mbc6ltauOqJ9ZR2dDi9DY8xWf5VYQE+un6AS60ICuBtk7b8bUbfNHn+VXc/sImpiRH8+KyeSRGOf/U5MyECF65dT7zMuP4yavbeHhVvltfqOfzIVDVaP9mvqGklj99awbfPWPssJ7fPys1huduzqW6qZUbn9lAU6tvfiv7LL+K+ZlxwxK2qne5GbEEBfixOt8zuimcbdP+Or77/EbGJUbyzA25wzoWFRUSyNM3zuHy2Sn8v4/28d9v7MBmc88g8OkQqGps5VtPrKWwqom/XZ/DJTNPtDSy88xMjeGxb89iz+FGvv/PTXR02lzSrrsorTlKcfVRzhivS4i6UkigP3MzYn1yXKCsrpllz+WRGBXMczflEh02/CcjBPr78dDl0/j+mWN5Yf1+fvraNjrdMAh8NgTqm9u59smvOHSkhedvnstZExJd2v5ZExL59SVT+Dy/it+9t8elbVvts3z7h9AZLt7nyj4usK+yyadOTjja2sF3ns2jtd3Gk9fnkBAZ7LK2RYQff2MC/3FOFq9sLOPHr251uyDwyRA42trBDc+sp6jqKE9cN9uyfumrclO5fn4af/+imOVbD1pSgxU+21tFWlwYGfHhVpfic053HH2t9pAzV4bKGMNdr28nv6KRR6+eybhE553sMVAiwp3njudHC8fz+qZyfvLqNrfqGvK5EGhp72TZ83lsK6vnkaUzWZBlbZfEPRdkMyc9hp++uo19FY2W1uIKrR2dfFlYo11BFpmQFElCZLDPhMDLeQd4e+tB7jx3PGdafOR5x8IsfrRwPK9tKuP+d3a5zWCxT4VAe6eN21/YzJqCGh785jQWTRlpdUkEBfjx2NWzCA3y544Xt9Da0Wl1ScMqr6SOY+2dGgIWEREWZMXzxb4qt+uWcLb8ikZ+sXwnp46L49Yzx1ldDgD/cc44vnNaBs98WcLDH+6zuhzAh0LAZjP85NVtrNpVwf0XT+abs1OsLum4xKgQHvzmNHYdauCPH+RbXc6w+nRvJUH+fjp1tIXOmpBIXXM7m/fXWV3KsGlp7+S2f20iIjiAh781w20mcRQR7rlgElfmpPDIR/v4++oiq0vyjRAwxnDv8h28sbmcH39jAtfNT7e6pK9ZmJ3E1XNTeWJ10fE1d73RZ/lV5GbEEhakM5ZY5YwJCQT4CR/urrS6lGHzmxW7ya9o4g9XznC7acpFhN9eNo3zp47kV+/u5uUN1l5Q5hMh8ODKvfxj3X6+e0Ym3z9zrNXl9OlnF0wiIz6cO1/eSn1zu9XlON3BI8fIr2jSriCLRYUEMjczlg93V1hdyrBYW1jDc2tLufHUdLd9r/n7CQ9/awYLsuK56/VtrNh+yLJavD4EHv+0gD9/Wsi356Zy16KJbr3QS1hQAP/vWzOpamrlV+/usrocp/t4j/2b55kT3PMP05csnJREQWUTJV622lhzWwc/fW0baXFh/OQbE60u54SCA/z567WzmZkawx0vbrZsriGnhICILBKRvSJSICJ39fJ8sIi85Hj+KxFJd0a7/Xl+bQkPvr+XS2aM5oGLp7h1AHSZmhLNstMzeWVjmcdMQDVQq3ZVkB4XxrhEz5tz3dssnJQE4HVHAw+t3Mv+2mYe/OY0QoPc/2r0sKAAnrp+DmMTIlj2fB5bDhxxeQ1DDgER8QceAxYD2cBSEcnusdnNQJ0xZhzwMPD7obbbnzc2l/Hzt3ZybnYSD10x3aMW0rjjnCwy4sO5+41tXjPZV1NrB2sLazg3O8kjwtjbjYkNY0JSJB950bjAhpJanvmyhOvnpzE303NOPIgOC+S5m3KJiwjixqfXU1Dp2lPFnXEkkAsUGGOKjDFtwIvAxeIwyEoAABLOSURBVD22uRh41nH7VeAcGcZPgpU7D/Nfr2zj1HFxPLp0pqULPJyMkEB/fnfZVA7UHvOas4U+21tFW6eNc7OtPy1X2Z0zKZH1JbVeMf7U3mnjv1/fTvKIUH6yyL27gXqTGBXCP26ei7+fH9c+uZ5yF84y7IxPx2Sg+/B2meOxXrcxxnQA9cCwRHVBZRO3/2sz01KieeLaHI+doGxuZhxXz03lqTXFbCtz/SGis63adZjY8CBmp3nuWqzeZmF2Ep02w6f5nn808PSaYvZVNvHLJZMJD/bMM8/S4sJ57qZcmhzTXLjqOg63+oosIstEJE9E8qqqTm6Sq7EJ4fzswkk8c0Oux74Zuty1eCJxEcH87M0dHn1hT3unjY/3VHL2xES3OV9bwYyUEcRHBHl8l9Ch+mP86cN9LJyUyDmOsQ5PlT06iqdumMPPL5zksr8VZ4RAOTCm2/0Ux2O9biMiAUA0UNPzhYwxTxhjcowxOQkJJ3cGiYhw3fx0l8wSONyiQgL52QWT2FZWz0sWn0s8FBuKa2lo6eDcbM/+A/U2fn7C2RMT+WRvJW0dnjuT7a/f3U2nzfCLiyZbXYpTzEmP5RQXrrjnjBDYAGSJSIaIBAFXAct7bLMcuN5x+3LgY+MuE2e4uSXTRzM3I5YHV+6h9mib1eWclHe3HyI00J/TLZ6nSX3doikjaWzpYE2hZ56Jtqagmne2HeIHZ41jTGyY1eV4pCGHgKOP/zZgJbAbeNkYs1NE7heRJY7NngTiRKQAuBP42mmkqnciwgOXTKGxpYOHVnrelNMdnTbe33GYcyYlesQpe77mtHEJRIYE8O426y5WOlltHTbufWsHaXFhLDs90+pyPJZTxgSMMSuMMeONMWONMb92PHavMWa543aLMeYKY8w4Y0yuMcb6CTM8yPikSG46NZ0XNxzwuPleviqupeZoGxdOG2V1KaoXQQF+nJc9kpU7D3tcl9CTXxRTWHWU+5ZM9tgTQNyBWw0Mq77dsXA8iZHB3PvWTo8aJH5n2yHCgvwtn8ZX9e3CaaNobOngiwLPWXHs4JFjPPLRPs7LTnL5glDeRkPAQ0QEB3DPBdlsL6/nX+v3W13OgNi7gg5xzqQk/abmxk4dF09USADveFCX0K/e3YXB8PMLe16XqgZLQ8CDXDRtFPMz43jo/T3UNLVaXU6/viysoa65nQumaleQOwsK8OMbk0eyamcFLe3uv57F5/lVrNh+mNt0MNgpNAQ8iH2QeDLNbZ38/n33HyR+Y3M5kSEBOmGcB1gyYzSNrR1uf81Aa0cnv1i+k4z4cG7RwWCn0BDwMOMSI7l5QQYv55WxsbTW6nL61NTawfs7DnPhtNHaFeQBThkbz8ioEF7bVGZ1KSf099XFFFfbB4ODA/R95QwaAh7oP87OYlR0CD9/cycdne55RseK7Yc41t7J5bN7ziCi3JG/n3DprGQ+y6+iqtE9uxrL6pp59ON9LJ4y0m3XCfBEGgIeKDw4gJ9fmM2uQw38Y12p1eX06vVNZWTEhzMrVecK8hTfnJVMp83w1paeF/y7hwfe2YUg/EwHg51KQ8BDLZ4ykgVZ8fzhg3wqG1usLuffHKhtZl1RLZfNTNZpoz3IuMRIpqdE8+pG9+sS+mRvJSt3VnD7OeNIHhFqdTleRUPAQ4kIv1wymZaOTn63wr0GiV/ZWIYIXDpLu4I8zeWzU9hzuJGtFixu0peW9k7uW76TzIRwvnOaDgY7m4aAB8tMiGDZ6Zm8vrmcr4q+Nh+fJdo6bLywfj9nTUgkJUZP3/M0F89MJizIn+fdqJvxfz8uoLSmmV9dMoWgAP3Icjbdox7utrOySB4Ryr1v7aTdDQaJP9h1mKrGVq6dl2Z1KeokRIUEcunMZN7eepA6N5iwsKCykb9+XshlM5NdOrOmL9EQ8HChQf784qJs9lY08uyXJVaXw3NrSxkTG6pnb3iwa+en0dph45WN1k5fbozhnjd2EBYUwH9fMMnSWryZhoAXODc7ibMmJPDwqnwqGqwbJN57uJH1xbVcMzfNo9Z0Vv9u4sgoctNj+ce6/dgsnKfq1Y1lfFVcy12LJxIfEWxZHd5OQ8ALiAj3LZlMu81w71s7sGqphr+vLiIk0I8rcsb0v7Fya9edksb+2mY+2FVhSfu1R9v4zYrd5KTF8C19Pw0rDQEvkRYXzo8Wjmflzgre3e76icDKjxzjjc3lXDUnldjwIJe3r5xr8ZRRpMeF8finBZZ8qfjtit00tnTwq0un6FHlMNMQ8CK3LMhgWko0v3hrp8snmPvb5/YlInQ+F+/g7yd894yxbCur54sC16469smeSl7ZWMYtp2cycWSUS9v2RRoCXiTA34+HLp9OQ0s79729y2XtVje18sL6/Vw6M1kv5PEil81KJikqmMc/KXRZm0ea2/jpa9uYkBTJDxdmuaxdX6Yh4GUmjIzk9rOzeHvrQd7fcdglbf7l00LaOm1878yxLmlPuUZwgD+3LMhkbVENawtdcx3Kz9/aSe3RNv5w5XSdIM5FNAS80K1njmXy6Cjufn0bh+uH92yh0pqjPLu2hCtmpzA2IWJY21Kud828NJJHhPLrFbuG/Uyhd7Yd5O2tB7njnCymJEcPa1vq/2gIeKFAfz8eWTqTlnYbP3ppy7AuR/n79/cQ4OfHf543YdjaUNYJCfTnx9+YwI7yBt4cxonlyuqaueeNHUxPieZWPaJ0KQ0BLzU2IYJfXjyZtUU1/O/HBcPSxoaSWlZsP8z3zhhLUlTIsLShrLdk+mimpUTz0Mq9NLd1OP31Wzs6+cG/NmOzGR5ZOpMAf/1YciXd217sitkpXDozmYc/zOdDJ5/v3dLeyU9f28bo6BBuOT3Dqa+t3Iufn/DzC7M5VN/Cg+/vdfrr//rd3Ww9cISHrphOWly4019fnZiGgBcTEX572VSmJkfzw5e2UFDZ6LTX/p+VeymqOsqDl08nLCjAaa+r3NOc9FhuOCWdZ74s4ctC550y+tzaEp5bW8otCzJYNGWk015XDZyGgJcLCfTnr9fOJiTQj+uf2sCh+mNDfs11RTU8uaaYa+elcVqWTurlK366aCIZ8eH8+JVt1B9rH/LrfbS7gvuW72ThpCTuWqxzA1llSCEgIrEiskpE9jn+/9oyUiIyQ0TWishOEdkmIt8aSptq8EaPCOXpG3KpP9bONX//akgXkpXWHOX7/9xEelw4dy2e6MQqlbsLDfLnD1dOp6KhhR/8c9OQZq1dU1DND/61icmjo3lk6Qz89apgywz1SOAu4CNjTBbwkeN+T83AdcaYycAi4E8iMmKI7apBmpoSzZPX51BWd4yrnlhH+ZHBHxEcaW7jxmc2YDOGp26YQ3iwdgP5mlmpMfz2sql8UVDNz944uXmqPt1byU3PbCA9Lpynb5yj3YkWG2oIXAw867j9LHBJzw2MMfnGmH2O2weBSkDnGbbA3Mw4nr5xDocbWrj0sTVsL6sf8M9WN7VyzZNfUVZ7jL9dl0NGvA7g+aorcsZw+9njeCnvAPct3zng6weMMTz5RTHfeTaPcYkRvHDLPJ0d1A0MNQSSjDFds5UdBpJOtLGI5AJBQK/XoYvIMhHJE5G8qqqqIZamenPK2Hheu/UUAv39uPTxNTy8Kp+2jhMf1m8oqWXJo19QUNnEX6+bzZz0WBdVq9zVneeOZ9npmTy7tpQbntlAZT9TmJcfOcat/9jEA+/s4uyJibywbB4xOtGgW5D+DudE5EOgt2H7e4BnjTEjum1bZ4z52riA47lRwKfA9caYdf0VlpOTY/Ly8vrbTJ2kuqNt3P/OLt7YXE56XBg3n5bBoimjSIi0fzOz2QybD9Tx7JelLN96kJSYUP787dlMTdErOZWdMYYX1h/gvrd3Euzvx42nZXD5rBRS48KOP59f0cTLeQeOL1f5X+eN55YFmYjoGMBwEZGNxpicAW8/lGliRWQvcKYx5lDXh7wx5muXjopIFPYA+I0x5tWBvLaGgGt8sreSP36Qz/Zye9dQYmQwYUH+VDS0cqy9k/Agf647JZ3bzhqnYwCqV8XVR/nNit2sclyLEhceRFRoINVNrTS2dOAncOnMFO48b7xOMOgCrg6Bh4AaY8zvROQuINYY85Me2wQB7wFvG2P+NNDX1hBwHWMMuw41sHpfNYWVTbR22IiLCGLGmBGcNTGRqJBAq0tUHuBAbTMf7q5g7+FGmlo7iAkLYvLoKM6elEhipF5R7iquDoE44GUgFSgFrjTG1IpIDvA9Y8x3ROQa4GlgZ7cfvcEYs+VEr60hoJRSg+fSEBhOGgJKKTV4gw0BvWJYKaV8mIaAUkr5MA0BpZTyYRoCSinlwzQElFLKh2kIKKWUD9MQUEopH+a21wmISBX2C9B6igect7TR8HD3GrW+oXP3Gt29PnD/Gj21vjRjzIBnanbbEOiLiOQN5kIIK7h7jVrf0Ll7je5eH7h/jb5Sn3YHKaWUD9MQUEopH+aJIfCE1QUMgLvXqPUNnbvX6O71gfvX6BP1edyYgFJKKefxxCMBpZRSTqIhoJRSPswtQ0BErhCRnSJicyxQ0/25u0WkQET2isg3+vj5DBH5yrHdS47VzYaz3pdEZIvjX4mI9LpgjuO57Y7tXLZYgojcJyLl3Wo8v4/tFjn2a4FjpThX1feQiOwRkW0i8oaIjOhjO5fvv/72iYgEO37/BY73XLor6nK0PUZEPhGRXY6/lzt62eZMEanv9ru/11X1Odo/4e9M7B5x7L9tIjLLxfVN6LZvtohIg4j8sMc2Lt2HIvKUiFSKyI5uj8WKyCoR2ef4v6+13K93bLNPRK4fUIPGGLf7B0wCJmBflzin2+PZwFYgGMgACgH/Xn7+ZeAqx+2/ALe6sPY/APf28VwJEG/B/rwP+K9+tvF37M9MIMixn7NdVN95QIDj9u+B37vD/hvIPgG+D/zFcfsq4CUX1jcKmOW4HQnk91LfmcA7rn7PDfR3BpyPfflZAeYBX1lYqz9wGPvFVpbtQ+B0YBawo9tjDwJ3OW7f1dvfCBALFDn+j3HcjumvPbc8EjDG7DbG7O3lqYuBF40xrcaYYqAAyO2+gYgIcDbQtaD9s8Alw1lvj7avBF5wRXtOlgsUGGOKjDFtwIvY9/ewM8Z8YIzpcNxdB6S4ot0BGMg+uRj7ewzs77lzHO+DYWeMOWSM2eS43QjsBpJd0bYTXQw8Z+zWASNEZJRFtZwDFBpjepupwGWMMZ8DtT0e7v4+6+sz7RvAKmNMrTGmDlgFLOqvPbcMgRNIBg50u1/G19/0ccCRbh8qvW0zXBYAFcaYfX08b4APRGSjiCxzUU1dbnMcbj/Vx6HkQPatK9yE/Zthb1y9/wayT45v43jP1WN/D7qUoxtqJvBVL0/PF5GtIvKeiEx2aWH9/87c5X0H9iO5vr7AWbkPAZKMMYcctw8DSb1sc1L7MmDotZ0cEfkQGNnLU/cYY95ydT39GWC9SznxUcBpxphyEUkEVonIHkfqD2t9wJ+BB7D/QT6AvcvqJme0O1AD2X8icg/QAfyzj5cZtv3nyUQkAngN+KExpqHH05uwd280OcaC3gSyXFieR/zOHOOGS4C7e3na6n34b4wxRkScdm6/ZSFgjFl4Ej9WDozpdj/F8Vh3NdgPKQMc38x622bQ+qtXRAKAy4DZJ3iNcsf/lSLyBvbuBqf8QQx0f4rI34B3enlqIPv2pA1g/90AXAicYxwdnL28xrDtvz4MZJ90bVPmeA9EY38PuoSIBGIPgH8aY17v+Xz3UDDGrBCRx0Uk3hjjkonRBvA7G9b33SAsBjYZYyp6PmH1PnSoEJFRxphDju6yyl62Kcc+ftElBfu46gl5WnfQcuAqxxkZGdjTeH33DRwfIJ8Alzseuh5wxZHFQmCPMaastydFJFxEIrtuYx8M3dHbts7Wo4/10j7a3QBkif3MqiDsh8bLXVTfIuAnwBJjTHMf21ix/wayT5Zjf4+B/T33cV8h5myOsYcngd3GmD/2sc3IrjEKEcnF/jfvkpAa4O9sOXCd4yyheUB9t24PV+rzKN7KfdhN9/dZX59pK4HzRCTG0eV7nuOxE3PViPcgR8cvxd6f1QpUACu7PXcP9jM29gKLuz2+AhjtuJ2JPRwKgFeAYBfU/AzwvR6PjQZWdKtpq+PfTuzdIK7an88D24FtjjfTqJ71Oe6fj/0Mk0IX11eAvS9zi+PfX3rWZ9X+622fAPdjDyyAEMd7rMDxnst04X47DXsX37Zu++584Htd70XgNsf+2op90P0UF9bX6++sR30CPObYv9vpdjagC+sMx/6hHt3tMcv2IfYwOgS0Oz4Hb8Y+zvQRsA/4EIh1bJsD/L3bz97keC8WADcOpD2dNkIppXyYp3UHKaWUciINAaWU8mEaAkop5cM0BJRSyodpCCillA/TEFBKKR+mIaCUUj7s/wNjDjVtAN9BKgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6KV7RqMm1d8P",
        "colab_type": "text"
      },
      "source": [
        "Plot $\\sin(x)$ and its spectrum, $\\cos(x)$ and its spectrum in a single plot, in the domain $[-2\\pi,2\\pi]$. Label the plot appropriately."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-OJuY0HO12Oo",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "554c8e31-9bc9-41aa-c4eb-08f524b8a4aa"
      },
      "source": [
        "#!pip install django\n",
        "x= np.linspace(-2*np.pi,2*np.pi,200)\n",
        "y= np.divide(np.sin(x),x)\n",
        "y_1=np.divide(np.cos(x),x)\n",
        "fig = plt.figure()\n",
        "plt.subplot(1,2,1)\n",
        "plt.plot(x,y)\n",
        "plt.subplot(1,2,2)\n",
        "plt.plot(x,y_1)\n",
        "ax1 = fig.add_subplot(121)\n",
        "ax2 = fig.add_subplot(122)\n",
        "ax1.title.set_text('Sin(x)')\n",
        "ax2.title.set_text('Cos(x)')\n",
        "plt.show()\n",
        "\n"
      ],
      "execution_count": 285,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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qBUVssamSp01EMgmH/f2q+nPv4eMiMl9Vj4nIfKB1steq6j3APQD19fWWXjNkbfhu2JW2CWRwJMTe490xb7+PWDW/iKOdA5zqHYrL8ZKZhN+BvwvsUtWvjntqI3Crd/tW4BfxLltKs8nTnLLATyB7W3oYDimvi/EInYjIG8vOY9asMw2XAx8E3iIiL3tf1wFfBK4WkX3AVd5948jpcfg+FyRFOGnSMW5sPxqe6iDWHbYRq7yZOHcc7eTypTZo6mxU9Y/AVO1sV8azLOlk7EpbG6bjhNXwE8iuY10UZGdQU5IXl+OV5mcxvzjHRuqYhDXWaWsLtDlhgZ9Adrd0s7yygEAg9h22EavmF9lIHZOw7EpbtyzwE4SqsqelmxXz4tOcE7F6QRGNbT0MDIfielxjpmNsiUPLeycs8BPE8a5BOvuHWTmvMK7HXbWgiFENf7owJtFYG75bFvgJIrKoeLwDf6X3iWKvBb5JQKcvvPK1GCnDAj9BRGrYK+PcpFNTmkdOZoA9xy3wTQKyqRWcssBPEHtauplXlENxXmZcjxsMCMsqCtlrgW8SmOW9Gxb4CWJ3Szcr4tycE7G8spA91qRjEpDNpeOWBX4CGA6N0tjaw8r5/gT+ynmFtHYP2hQLJuHYsEy3LPATwMETvQyFRuPeYRux3DuuteObRBOZQ8fy3g0L/AQQ6bBdURnfDtuIFZXhwLd2fJNoIjlvge+GBX4C2N3SRTAg1FXk+3L8yqJsinIyrB3fJBxr0nHLAj8B7GnpZklZPtkZQV+OLyKsmGcjdUzisRq+Wxb4CWB3Szcr5/vTnBMRGalj846bRGJLHLplge+znsERjpzq963DNmLFvEK6BkY43jXoazmMmYxdaeuGBb7PIs0okY5TvyyvtJE6JvGMzaVjNXwnLPB91nC8B4BllQW+liMS+DanjklE1qTjhgW+zxrbesjKCFAdp0VPplKan0V5YbbV8E1CsSUO3bLA91lDaw9LyvIJxnHRk6mstJE6JsHYsEy3LPB91tDWQ12Fv805Ecsrw4EfsuqUSRD6mhsmGk4CX0SuEZE9ItIgIndNsc2fichOEdkhIj9xcdxkNzAcoqm9j6XliRH4yyoKGBgepflUv99FMQawGr5rGdHuQESCwN3A1cARYIuIbFTVneO2WQZ8GrhcVU+JSEW0x00FB0/2MqokTA1/qVeOhrZuFs71t0/BGLA2fNdc1PAvBhpUdb+qDgEPABsmbPNR4G5VPQWgqq0Ojpv0Glt7ARKmhj8W+K09PpfEmDBb4tAtF4FfBTSNu3/Ee2y85cByEXlaRDaLyDWT7UhEbheRrSKyta2tzUHREltDaw8isKTcnzl0JpqTl0VZQZYF/hRE5Hsi0ioi28c9Vioij4nIPu97iZ9lTFVWw3cjXp22GcAy4M3AjcC9IjJn4kaqeo+q1qtqfXl5eZyK5p/Gth6qS3LJyfRnDp3J1JUX0NjW63cxEtUPgImVlbuAJ1R1GfCEd984Erngajg06nNJUoOLwG8Gasbdr/YeG+8IsFFVh1X1ALCX8BtAWmto7aEuQZpzIpZWFNDQ2mNXNk5CVZ8C2ic8vAG4z7t9H/CuuBYqxZ2+0tZC3wUXgb8FWCYii0UkC7gB2Dhhm/8kXLtHRMoIN/Hsd3DspDU6quw/0ZMw7fcRdeUFdPYPc6LHVr+apkpVPebdbgEqJ9so3ZorY6F3cMTvIiS9qANfVUeAO4FHgF3Ag6q6Q0Q+JyLXe5s9ApwUkZ3Ak8DfqurJaI+dzJo7+hkYHk2YEToR1nE7exr+WDTpR6N0a650Zfwvs8cCP2pRD8sEUNVNwKYJj3123G0FPul9GcIXXMHpgE0Up4dm9nBZ3VyfS5MUjovIfFU9JiLzARuB5tD4lkUL/OjZlbY+afRq0InWpDO/OIf8rOBY+cw5bQRu9W7fCvzCx7KknPHDMa1JJ3oW+D5pbOuhND+Lkvwsv4tyBhGhzuu4NWcSkZ8CzwIrROSIiHwY+CJwtYjsA67y7htHzqzhh/wrSIpw0qRjZq6xtTfhavcRS8sLeKYxrbtYJqWqN07x1JVxLUgaOaMNf8Bq+NGyGr5PwpOmJcYFVxPVVRTQ0jVA98Cw30Ux6U6tScclC3wftPcO0d47lHBj8CMiHbd2AZbx2/gafrcFftQs8H3Q6I3QSbQhmRE2NNMkivFt+FbDj5614fugIUFH6EQsKs0jMygW+MZ3ihIMCBkBscB3wGr4Pmhs7SEnM0DVnFy/izKpjGCA2rn5FvgmIQhQkJ1hTToOWOD7oKGthyVlBQQSYFnDqSytKBhrejLGL5EmncKcDLr6bRBBtCzwfdDQ2pNwV9hOtLSigEMnexkcsbHPxj8KiEBlUQ4tnQN+FyfpWeDHWf9QiOaO/oQdoROxtKKAUYWDJ/r8LopJY6ogCFUluTR32NKb0bLAj7P9J3pQTbw5dCaKvCFZO77xk6IgUF2Sx/GuAZsiOUoW+HEWGdueqBddRdSVFyBigW98Fs57qufkMqpYs06ULPDjrKG1h4BA7dzEDvzcrCBVc3Kt49b4KtKGX1USHtF25JQ160TDAj/OGtt6qCnNS6hlDacSXu7QAt/4R1URhIWleQB2PkbJAj/OGlsTb5WrqUSGZo7aCtLGJ6rhGn51SS6l+Vm80tThd5GSmgV+HIVGlf0nehO+wzairryAgeFRjnbax2jjDyXchi8irK2Zw8sW+FGxwI+jI6f6GBoZTfghmRE2p45JBCLhCxTX1cyhoa2Hkz2DPpcoeVngx1EkOBN10rSJ6srDHcs2a6bxy/jJ095yXgWq8MiO4/4VKMlZ4MdRpMMpWdrwS/OzmJOXaR1lxjeKEpmAZNX8IhaX5fPQS0d8LVMys8CPo4bWHsoKsinOy/S7KNMiIiwtt+UOjX800ohP+Hy8+dJFbDl4ihcOtftarmRlgR9HjW29Y80kyaKuvID9VsM3Pho/xeAN62soL8zmf27cwdCIXXU7Uxb4caKqSTFp2kRLKwo40TNER9+Q30UxaUhVxzptAfKzM/jc9avZ3tzFXT/fhqoNGZ4JC/w4OdEzRGf/cNIFfmQKCGvHN36IXGk73rWvm89/uWo5P3+xmU///FWb0XUGnAS+iFwjIntEpEFE7jrLdu8VERWRehfHTSZjyxomSYdtRKS8ja02UsfEn+qZTToRf3XlUu78k6U8sKWJd9/9jLXpT1PUgS8iQeBu4FpgFXCjiKyaZLtC4K+B56I9ZjIaW9YwyWr41SV5ZGUEaLAa/pSmW+ExM6ec2aQTISL817et4N5b6jnZO8h7/+VZPnDvZh7d0WIzap6FizVtLwYaVHU/gIg8AGwAdk7Y7vPAl4C/dXDMpNPY1kNeVpD5xTl+F2VGggFhSVk+jTZSZ1LjKjxXA0eALSKyUVUnnv++GhoZpXtgmM7+YboGRugeGKZnYISewRF6B0foHQqFvw+O0DMYYnAkxKgqodHTX6MKWRkBcjOD5GSGv+dmZTA3P4vywmzKCrIpL8xmYWkeuVlu5oqaqoYfcfWqSl5fN5f7nj3Ij549xO0/eoHi3EyuOq+SNy4vo762NGGXEp3M0Mgo/UMhRkZHCY0qI97vPvx9lMh7mQgsKcsnIzizOruLwK8CmsbdPwJcMn4DEbkQqFHVX4vIlIEvIrcDtwMsXLjQQdESR0NrjzflcOIuaziVuooCtjd3+l2MRDXdCs85HT7ZR+/QCKOqqIbDblTV+4Lh0Cj9wyEGhkL0D4e/BoZHGRgO0Tc0QvfACF1eoHf2D3u3h+nqH6F/+Nzt3BkBIT87g4LsDLIzAgQCQlCEYCD8FRAYHAkfb2B4lIGREH2DIYYmqVEvKM5hSXkByysLWbdwDusWzqFqTu6szv9zvSQ/O4OPv3kpt79hCU/uaePh7cd4bGcL//HikbGynDe/iKWVBSyvKKS2LI+KwhwqirLJznDzxhQaVbq933VX5I113O+/c+z2sPcmG/6b9Q6F6PPecPuGRhgOTb8T+oW/v4q5BdkzKqeLwD8rEQkAXwVuO9e2qnoPcA9AfX19SnW/72/rZX1tid/FmJW68gIefvUYA8OhpJjlM87OWeGB6VVmPvngy2w9dGpWhQgGhKKcDIpyMynKyaQoN4OKwgKKcjIpzst8zXOFOZkUZGeQn5VBfnaQfC/kZxrIqkr34Aht3YO0dQ/S2j3IwRO97G/rYf+JXn7y/CG+9/QBAGpKc7nqvEquXlXJJYvnEpzGms4zCYGMYICrV4X3HxpVdh3rYsvBdl483MHelm6e2tf2mkCdk5fJ3Pws8sf9LnIyg4jI2CcLkXCgR95cB8bebEP0D4XoHhg55wLrAYHCyO8+O5P87CBz8rKoKgmSl5VBflaQvOzw95zMIJnBABlBISMgBAMB77sQmDBiaaZcBH4zUDPufrX3WEQhsAb4nXcyzQM2isj1qrrVwfETXu/gCM0d/dxYUXPujRPQ2HKHJ3tZOa/I7+IkpelUZj711hV09g+NhU1AhECAsfuR5pTcrGD4e2aQbO97ZlB8+fQoIuE3kZzMSQckDIdG2dPSzQuHTvH7vW3c/9xhvv/0QapLcrn1slpuuLiGwpypL0QMj7qc+c8VDAhrqopZU1XMhy4/XZZDJ/s4cqqP1q5BjncNcLx7gPbeobEa99GOYQaGQ2NvNJFhnwERciJNWVlBinMzyfH+DpE30fD3TIpzx73BerfzszIITOMNLtZcBP4WYJmILCYc9DcAH4g8qaqdQFnkvoj8Dviv6RL2EK7dQ/J12EaMzanTaoE/iXNVeKbtsrq5TgqUSDKDgbHgvfX1tfQOjvDb3a386NlDfGHTLr791H7+7rqVvHtd1RRvWHrOJp2ZlGVpRUHS/h+6EPUoHVUdAe4EHgF2AQ+q6g4R+ZyIXB/t/lNBsg7JjFhSFl7u0MbiT2qswiMiWYQrPBt9LlPCys/O4J0XLODBOy7joY+/noWluXzywVf4bz/bxsAk/Qzn6rQ1M+OkDV9VNwGbJjz22Sm2fbOLYyaThtYeggFhUYIvaziVyHKHNqfOa6nqiIhEKjxB4HuqusPnYiWFdQtL+Pc7Xs//fXwv3/htAyd7h7jngxedMfIksgCKccOutI2DxrYeFpWGx7MnK1vucGqquklVl6tqnap+we/yJJNgQPjkW1fw+Xet4be7W/nnR/ee8Xx4tkxLfFeSN4GSSENrT9LMgT8VW+7QxNIHL13E++truOepRnYcPT0E2Gr4blngx9hIaJSDJ3uTtv0+wpY7NLH2d9edR0F2Bt94Yt/YY+NmRzYOWODH2OH2PoZDmvQjA2z1KxNrxXmZ3HJZLY/sOE5zR7hiEa7hW+S7YoEfY2PLGibZPPgT2fq2Jh7ed1E1AA+/esznkqQmC/wYi9SIk70N35Y7NPFQW5bPqvlFPLKjBQh32hp3LPBjrKG1h4rCbIrOcjVhMrDlDk28XFY3l1eOdIZXtLJOW6cs8GOsobWbZZXJXbuPsOUOTTysrZnD0Mgou1u6Jl0AxcyeBX4MqSqNbb0sqyj0uyhO1FXk23KHJubW1swB4JWmjvAShzZOxxkL/Bhq6RqgZ3Ak6dvvIyIdt9aOb2KpuiSX3MwgB070WQ3fMQv8GNp33FvlKsnH4EfYcocmHkSEqpJcmjv6bC4dxyzwYyjSwZkqbfi23KGJl6o5uTR39Hs1fIt8VyzwY2hfa8/YAgupwJY7NPFSVZJL86l+rw3fuGKBH0ONrT0sq0jOZQ2nUldRYDV8E3NVc3I51TdM31DI2nQcssCPoX2t3Uk/pcJEdeUFNLX3TTp3uTGuRBYeP9rRb3nvkAV+jJzsGeRU3zBLU2RIZkRdef7YcofGxEpxbvhCxe6Bs68Va2bGAj9G9nnt3KlWwx8bmmkjdUwMFeSE12bqHhhOqSZRv1ngx0hDiga+LXdo4iE/ywv8wRFr0nHIAj9GGlp7yM8KsqA4x++iOGXLHZp4KPRq+LYAilsW+DESWeUqFT+O2nKHJtbys08vt21TK7hjgR8jqThCJyIS+LbcoYmV/Ozg2O0UrDP5xgI/BroGhjneNZiygb+0wpY7NLGVnREkK2jx5Jr9RmMgciVqqsySOZEtd2jiIVLLT8VmUb84CXwRuSiHCPIAABWOSURBVEZE9ohIg4jcNcnznxSRnSKyTUSeEJFFLo6bqFJ1SGZE5Ofad7zb55LEh4j8qYjsEJFREamf8NynvfN+j4i8za8ypqLI0EyLe3eiDnwRCQJ3A9cCq4AbRWTVhM1eAupV9XzgZ8A/RXvcRNbY2kNWRoCakly/ixITcwuymZufNTYbaBrYDrwHeGr8g955fgOwGrgG+Jb3/2AciAzNtAq+Oy5q+BcDDaq6X1WHgAeADeM3UNUnVbXPu7sZqHZw3IS1r7WHJWX5ZKRwG+TyykL2pEkNX1V3qeqeSZ7aADygqoOqegBoIPz/YByIDM007rhIpCqgadz9I95jU/kw8PBkT4jI7SKyVUS2trW1OSiaPyJDMlPZinmF7DvejWpaj9SZ9rmfKud2PEWGZloN3524VkFF5GagHvjyZM+r6j2qWq+q9eXl5fEsmjMDwyGaTvWlzKInU1leWUjvUIjmjtQYqSMij4vI9km+Npz71eeWCud2vBVEAt9a8Z1x8ZmpGagZd7/ae+wMInIV8BngTao66OC4CWnf8R5UwzXgVLbcW9Rl7/FuqkvyfC5N9FT1qlm8bFrnvpmdrIxwfdRq+O64qOFvAZaJyGIRySLcibVx/AYisg74NnC9qrY6OGbC2t3SBaR+4C+rDP98e1rSpuN2MhuBG0QkW0QWA8uA530uU8oIeElvee9O1IGvqiPAncAjwC7gQVXdISKfE5Hrvc2+DBQA/y4iL4vIxil2l/T2tHSTnRGgdm6+30WJqeLcTOYX57A3DTpuReTdInIEuAz4tYg8AqCqO4AHgZ3Ab4BPqKotFOBIMFK1tyq+M066wVV1E7BpwmOfHXd7Nh+Xk9Ke490sqywgGEj9k3R5ZSF7WlI/8FX1IeChKZ77AvCF+JYoPQQCVsN3LXXHDfpkd0s3KyqL/C5GXKyYV0hDWw8joVG/i2JSUGRUs1Xw3bHAd6i9d4i27kFWpnj7fcTyykKGRkY51N537o2NmSFrw3fPAt+hSPNGqnfYRqzwOm73pkGzjom/scC3Kr4zFvgO7fFG6KRLDX9pRXj1q73pM8WCiaN06AeLNwt8h/Yc76YkL5Pywmy/ixIXuVlBFpXmpcVIHRN/kby32HfHAt+h3S3drJhXmFYfQZel0Zw6Jr7GRumkz79TzFngOzI6quxt6WblvPQYoROxorKQAyd6GRyx4efGreBYp60lvisW+I40d/TTOxRieWV6tN9HLJ9XSGhUaWy1xVCMWwGxNh3XLPAd2Z1mI3QizvN+3siUEsa4YhdeuWeB78ieNJlDZ6LFZflkZwTYedQC37gVadJJ6wm4HbPAd2TP8R6qS3LHpnRNFxnBACvnFbLzmAW+cSsySifN11xwygLfkT0tXWkz/n6iVQuK2Hmsy/4xjVORJh07rdyxwHegfyhEQ2sPq+an1widiFXzi+joG+ZY54DfRTEpJHLhVcgS3xkLfAd2t3QxqrC6qtjvovhi1YLwG5214xuXIm34o5b3zljgO7DDC7rVC9Kzhr9iXhEiWDu+cWrsgiur4Ttjge/AjqOdFOdmUjUn1++i+KIgO4PauflWwzdORZp0rIbvjgW+AzuOdrGmqiitplSYaNX8IqvhG6dOB74lvisW+FEaDo2yu6Wb1QvSs/0+YtWCIg6399E1MOx3UUyKiFSgLO/dscCPUkNrD0Mjo2nbfh8RGaG0y5p1jCOnO20t8V2xwI/S6Q7b9K7hR97wXm3u9LkkJlVElji0vHfHAj9KO452kpsZZHFZvt9F8VVFUQ7zinLYdsQC37ghVsN3zgI/SjuauzhvfqGtzgOcX13MtiMdfhfDpAibS8c9C/wohEaVnce6WJOmF1xNdEHNHA6e7KOzL7U6bkXkyyKyW0S2ichDIjJn3HOfFpEGEdkjIm/zs5ypZmyUjo3LdMZJ4IvINd4J3yAid03yfLaI/Jv3/HMiUuviuH5raO2hZ3CEC6rnnHvjNHB+dfiNLwXb8R8D1qjq+cBe4NMAIrIKuAFYDVwDfEtEgr6VMsUEbFimc1EHvneC3w1cC6wCbvT+Ecb7MHBKVZcCXwO+FO1xE8HLTacAWLvQAh/g/Krw7+GVFGvWUdVHVXXEu7sZqPZubwAeUNVBVT0ANAAX+1HGVDQ2W6a/xUgpLmr4FwMNqrpfVYeABwj/I4y3AbjPu/0z4EqZ5VVKqpowi2a/3NRBUU4Gi+emd4dtRHFeJrVz8xKmHb+htTsWM3j+OfCwd7sKaBr33BHvMeOADct0z0XgT+ekH9vGqyl1AnNnc7AfPHOQt339KZra+2bzcqdeOtzBBTVzxj56Gji/ek5CjNQ51TvEdd/4I197bO+0theRx0Vk+yRfG8Zt8xlgBLh/puURkdtFZKuIbG1ra5vpy9PSWJPOqM8FSSEJ1Wk7nX+Ka9bMIyDC/c8djnPpztQ7OMLe492sW1jiazkSzfnVxRzrHKC129+pkn/2whGGRkZ5+/kLprW9ql6lqmsm+foFgIjcBrwDuElPf2xoBmrG7abae2yy/d+jqvWqWl9eXj7bHyutBNJ4qpJYcRH40znpx7YRkQygGDg5cUfT+aeYX5zLlSsreHBrE4MjIQfFn51XmzsZVVhXY+33413g/T62NflXyx8dVe5/7hDra0ucLDkpItcA/w24XlXHf7TcCNzgDUpYDCwDno/6gAY4feGVNem44yLwtwDLRGSxiGQRHrWwccI2G4FbvdvvA36rUTSu3nzpItp7h3j41ZbZ7iJqLzeF26kvsMA/w5oFxWQEhBcPn/KtDE83nuDgyT5uvnSRq11+EygEHhORl0XkXwFUdQfwILAT+A3wCVX1rxaSYgLWhu9c1AuwquqIiNwJPAIEge+p6g4R+RywVVU3At8FfiQiDUA74TeFWbtiaRm1c/P48eZDvGudP31kLx/uYNHcPErzs3w5fqLKzQqypqqYrQf9C/z7Nx+mND+La9bMc7I/b3TZVM99AfiCkwOZMwRs8jTnnLThq+omVV2uqnXePwCq+lkv7FHVAVX9U1VdqqoXq+r+qAodEG66ZBFbD51id4s/k3W93NTBWqvdT2p9bQkvH+nwpcmtpXOAx3Yd50/rq8nOsCHxyczmw3cvoTptZ+J9F1WTlRHgx5sPxf3YTe19tHQNcKF12E6qvraUoZFRXvVhtM4DWw4TGlVuuthZc47xiTXpuJe0gV+Sn8U7zp/PQy820zM4cu4XOPTcgXYALllSGtfjJov6ReE3wi1xbtYZCY3ywPNNvHF5OQvn5sX12Ma9yGhnC3x3kjbwAT546SJ6h0I89NKkI+Fi5rn9JynJy2R5RfQjQFLR3IJs6srz2XqwPa7HfWJ3Ky1dA9x8ycK4HtfERqRJx/LenaQO/LU1c1i9oIj7Nx+KxRWVU9p84CQXLy61C67OYn1tKVsPnYrrxFc/3nyI+cU5vGVlRdyOaWLH5tJxL6kDX0S4+dJF7G7p5oVD8Wk+ONrRT1N7P5csntWFwmmjvraUzv5hGtp64nK8gyd6+cO+E9ywfiEZwaQ+rY0naKN0nEv6/4wNaxdQmJ0Rt87b5w6Erxe7dIkF/tmsrw234z9/ID7NOj99/jDBgHDDxTXn3tgkhdPDMi3xXUn6wM/LyuA9F1ax6dUWTvYMxvx4mxvbKc7NZKWDKzhT2cLSPOYX5/BM44mYH2tgOMSDW5t466pKKotyYn48Ex+BsStt/S1HKkn6wIfwlbdDoVEe3Hok5sd67sBJ1tda+/25iAiXLy3jmcaThGL8H/vw9mOc6ht2eWWtSQBBa8N3LiUCf1llIZcsLuUnzx+KaSfh0Y5+Dp7s41Ibjjktb1hWRkffMDuOxnY8/o83H2ZxWT6XWTNbSgnYEofOpUTgQ7iW39Tez+/3xW7q2d/vDe/7jctttsPpeH1dGQB/2Be7Zp1dx7p44dApbrpkoX3qSjHWhu9eygT+21bPo6wgm/tj2Hn7uz2tzC/OYVlFQcyOkUrKC7NZOa+QP8Yw8H/47EFyMgO876Lqc25rkkukSSfWTYLpJGUCPysjwA3ra/jt7laOnHK/OMrQyChPN5zkzSvKmeViXWnpTcvL2Xqone4B9wubn+od4ucvNvPuddXMybNJ7FLN6Stt/S1HKkmZwAe40bvC8qfPu18c5YVDp+gZHOFNy+2inpm4alUlwyHlqb3ua/kPbGlicGSU215f63zfxn+2AIp7KRX4VXNyecvKSn76fBMDw25navzt7uNkBoXLl1rH4ExcuLCEkrxMHt913Ol+R0Kj/OjZg7y+bq6TRU5M4glan4xzKRX4AB++YjHt3kd9V1SVh7e3cPnSMgpzMp3tNx0EA8JbVlby292tjITcLU762M7jHO0csNp9CrPAdy/lAv/SJaWsqSriu3/c72yI5o6jXRw51c91a+Y72V+6uXpVBZ39w06vuv3+0wepLsnlyvMqne3TJBZr0XEv5QJfRPjIFUtobOvld3tbnexz06vHCAaEq1dZuMzGm5ZXkJ8V5JfbjjrZ38tNHTx/sJ1bL6u1WmAKC1riO5dygQ/w9vPnM784h3ueimphLSDcnLPp1WNcuqSUElvOcFZys4K8bfU8fr3tmJNVsL752waKczPHOulNarI3c/dSMvAzgwE+fMViNu9vj7oZYcvBUxw82ce719k472hcv3YBXQMj/H5PdBfG7W7p4vFdx/nQ5bUUZEe9JLNJYDb82b2UDHyAmy5ZRHlhNl97bG9U+3lwaxP5WUGue52bBbHT1RVLy5ibn8V/vBjdfEd3P9lIflbQOmvTgNXw3UvZwM/NCvKxN9Xx7P6TbN5/clb76Bkc4dfbjvHOCxaQl2W1yWhkBAP8aX0Nj+9q5WhH/6z20dDaza+3HeXmyxbZhVZpwNrw3UvZwAf4wCULqSjM5quP7Z3VfBw/29pE/3CI96+3OdZduOmShYyqcv9zs5v+4ku/2UNeVga3v2GJ45KZRGR5715KB35OZpC/vHIZzx9o55EdLTN67XBolHv/cID1tSWsW1gSoxKml5rSPK70LozrH5pZ5+3zB9p5bOdxPvbmOuYWZMeohJMTkc+LyDYReVlEHhWRBd7jIiLfEJEG7/kL41qwFGdNOu6ldOAD3Li+hpXzCvn8r3bN6OrbX75ylOaOfu54U10MS5d+bn/jEtp7h/jR5oPTfs1waJTP/mI784py+PPLF8eucFP7sqqer6prgV8Bn/UevxZY5n3dDvyLH4VLVdak415UgS8ipSLymIjs876/piosImtF5FkR2eHVgt4fzTFnKiMY4H++czXNHf185dE903rNwHCIrz2+l5XzCvmTFTZ3jksXLy7lTcvL+dbvGqc9odp3/nCA3S3d/OOG1eRmBWNcwtdS1a5xd/M5PUX7BuCHGrYZmCMidnWeIzbdtXvR1vDvAp5Q1WXAE979ifqAW1R1NXAN8HURmRPlcWfksrq53HTJQr7zxwPT6sD99u/309Tez2ffucpOuhj427etoKNvmK9OYwTV9uZOvvb4Xt66qpK3rfZvpJSIfEFEmoCbOF3DrwKaxm12xHtsstffLiJbRWRrW1vs1mww5myiDfwNwH3e7fuAd03cQFX3quo+7/ZRoBWI+woin3n7eSwqzeMvf/rSWadP3t7cybd+18A7zp8/toCHcWtNVTG3XraI7z99kGcapp5Fs6NviI/d/wJz87P4P+95XUzLJCKPi8j2Sb42AKjqZ1S1BrgfuHOm+1fVe1S1XlXry8ttAR3jj2gDv1JVj3m3W4Czzj0gIhcDWUDjFM/HrBaUl5XBvbfUMzAc4rbvb+FY52uHBrZ2DfDRH25lbn4W/3D9aqfHN2e669rzWFKWz1898BL7jne/5vmOviFu/u5zHO8c5JsfuDDmHbWqepWqrpnk6xcTNr0feK93uxkYP4Sr2nvMmIR0zsA/V80nQsPjHqcc++i1bf4I+JCqTjptYqxrQcsqC7n3lnqOdfRz/Tef5sndrWPDNZ/bf5L3/uszdPQNc++t9ZTFeSRIusnNCnLvrfWICDfeu5kn94T/FqrKH/a1cf03n2bv8R6+fctFXLTI31FSIrJs3N0NwG7v9kbgFm+0zqVA57gKkDEJ55xXE6nqVVM9JyLHRWS+qh7zAn3S2cpEpAj4NfAZr3PLN5cumctDn7icO370Ah/6wRbKCrLICARo6Rqgak4uP/noJaxeUOxnEdNGXXkBD9x+KR+9bysf+v4WyguzEaC1e5DFZfnc/5FLWF+bEAvGf1FEVgCjwCHgDu/xTcB1QAPhvqoP+VM8Y6Yn2stHNwK3Al/0vk/8+IuIZAEPER7N8LMoj+fE8spCfvM3b+RX247ybONJQqPKhYtKePe6KvJtfpa4qisvYNNfv4FfvnKU5w60owr1teG/RU5m/EfkTEZV3zvF4wp8Is7FSSuf37CatTV2HYwrEs2K8CIyF3gQWEi45vNnqtouIvXAHar6ERG5Gfg+sGPcS29T1ZfPtu/6+nrdunXrrMtmzLmIyAuqWh/v49q5bWLpbOd1VNVZVT0JXDnJ41uBj3i3fwz8OJrjGGOMiV7KX2lrjDEmzALfGGPShAW+McakCQt8Y4xJExb4xhiTJizwjTEmTVjgG2NMmojqwqtYEpE2whdzuVQGTD09Y/JL5Z8vFj/bIlWN+9SVdm7PmP1sMzPleZ2wgR8LIrLVjysr4yWVf75U/tlcSOXfj/1s7liTjjHGpAkLfGOMSRPpFvj3+F2AGEvlny+VfzYXUvn3Yz+bI2nVhm+MMeks3Wr4xhiTtizwjTEmTaRd4IvIP4hIs4i87H1d53eZoiUi14jIHhFpEJG7/C6PSyJyUERe9f5WtmrIWdi5nVz8OLfTrg1fRP4B6FHVf/a7LC6ISBDYC1wNHAG2ADeq6k5fC+aIiBwE6lU1VS+8ccbO7eTix7mddjX8FHQx0KCq+1V1CHgA2OBzmYxxwc5tx9I18O8UkW0i8j0RSfYVkquApnH3j3iPpQoFHhWRF0Tkdr8LkwTs3E4ecT+3UzLwReRxEdk+ydcG4F+AOmAtcAz4iq+FNedyhapeCFwLfEJE3uh3gfxk53ZKifu5HdUi5olKVa+aznYici/wqxgXJ9aagZpx96u9x1KCqjZ731tF5CHCH/Of8rdU/rFz287taKRkDf9sRGT+uLvvBrb7VRZHtgDLRGSxiGQBNwAbfS6TEyKSLyKFkdvAW0n+v1fM2LmdPPw6t1Oyhn8O/yQiawm3nx0E/sLf4kRHVUdE5E7gESAIfE9Vd/hcLFcqgYdEBMLn6k9U9Tf+Fimh2bmdPHw5t9NuWKYxxqSrtGvSMcaYdGWBb4wxacIC3xhj0oQFvjHGpAkLfGOMSRMW+MYYkyYs8I0xJk38f0Ohn7AKbiE9AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3eexf9tO4XK3",
        "colab_type": "code",
        "outputId": "b5fe10f8-0e0f-4e0a-b3a1-964c83126bca",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "# Loading the libraries \n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import seaborn as sns\n",
        "import scipy.stats as stats\n",
        "from matplotlib import pyplot as plt\n",
        "from math import pi\n",
        "# Refer to the official documentation of packages \n",
        "x = np.arange(-2*pi, 2*pi, 0.1)\n",
        "y = np.sin(x)\n",
        "plt.plot(x, y, 'o') # we can also try go/bo/ro/r- etc for changing the representation of the points (marker)\n",
        "plt.plot(x,np.cos(x))\n",
        "plt.legend(['sin', 'cos'])\n",
        "plt.show()\n"
      ],
      "execution_count": 287,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}