equation_gpt_train_statistics.jsonl

{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>f(x, \\lambda)=\\lambda e^{-\\lambda x}</equation> in Exponential Distribution is: PDF of Exponential Distribution.", "tag": "Math,Statistics", "prompt": "What does the symbol mean <equation>f(x, \\lambda)=\\lambda e^{-\\lambda x}</equation> in Exponential Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>f(x, \\lambda)=\\lambda e^{-\\lambda x}</equation> in Exponential Distribution is: PDF of Exponential Distribution.", "tag": "Math,Statistics", "prompt": "What is the meaning of the symbol <equation>f(x, \\lambda)=\\lambda e^{-\\lambda x}</equation> in Exponential Distribution?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean}\\\\ \\\\mu \\\\\\\\ \\\\text{Poisson Variance}\\\\ \\\\sigma^2=\\\\mu</equation>", "tag": "poisson,statistics", "prompt": "Please give me some hints on equation Poisson Distribution?"}
{"completion": " The Latex Code for equation Normal Gaussian Distributionis <equation>X \\\\sim \\\\mathcal{N}(\\\\mu,\\\\sigma^2) \\\\\\\\ f(x)=\\\\frac{1}{\\\\sigma\\\\sqrt{2\\\\pi}}\\\\exp{[-\\\\frac{(x-\\\\mu)^{2}}{2\\\\sigma^{2}}]}</equation>", "tag": "Math,Statistics", "prompt": "What is the equation of Normal Gaussian Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>\\lambda=\\frac{1}{\\mu}</equation> in Exponential Distribution is: The rate parameter.", "tag": "Math,Statistics", "prompt": "What is the meaning of <equation>\\lambda=\\frac{1}{\\mu}</equation> in Exponential Distribution?"}
{"completion": " The Latex Code for equation Exponential Distributionis <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>", "tag": "Math,Statistics", "prompt": "What is the equation of Exponential Distribution?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean}\\\\ \\\\mu \\\\\\\\ \\\\text{Poisson Variance}\\\\ \\\\sigma^2=\\\\mu</equation>", "tag": "poisson,statistics", "prompt": "Can you write equation Poisson Distribution?"}
{"completion": " The equation for Normal Gaussian Distribution is: <equation>X \\\\sim \\\\mathcal{N}(\\\\mu,\\\\sigma^2) \\\\\\\\ f(x)=\\\\frac{1}{\\\\sigma\\\\sqrt{2\\\\pi}}\\\\exp{[-\\\\frac{(x-\\\\mu)^{2}}{2\\\\sigma^{2}}]}</equation>. Here is the brief introduction of Normal Gaussian Distribution:\n        X denotes the random variable which follows the normal distribution. \\mu denotes the mean value and \\sigma denotes the standard deviation.\n    ", "tag": "Math,Statistics", "prompt": "What's the meaning of Normal Gaussian Distribution?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\ \\\\text{Poisson Variance} \\\\sigma^2=\\\\mu</equation>", "tag": "poisson,statistics", "prompt": "How to write equation Poisson Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>F(x, \\lambda)=1 - e^{-\\lambda x}</equation> in Exponential Distribution is: CDF of Exponential Distribution.", "tag": "Math,Statistics", "prompt": "Can you explain the symbol <equation>F(x, \\lambda)=1 - e^{-\\lambda x}</equation> in Exponential Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\alpha</equation> in Gamma Distribution is: Gamma function parameter.", "tag": "Math,Statistics", "prompt": "What is the meaning of <equation>\\alpha</equation> in Gamma Distribution?"}
{"completion": " The equation for Normal Gaussian Distribution is: <equation>X \\\\sim \\\\mathcal{N}(\\\\mu,\\\\sigma^2) \\\\\\\\ f(x)=\\\\frac{1}{\\\\sigma\\\\sqrt{2\\\\pi}}\\\\exp{[-\\\\frac{(x-\\\\mu)^{2}}{2\\\\sigma^{2}}]}</equation>. Here is the brief introduction of Normal Gaussian Distribution:\n        X denotes the random variable which follows the normal distribution. \\mu denotes the mean value and \\sigma denotes the standard deviation.\n    ", "tag": "Math,Statistics", "prompt": "Can you explain Normal Gaussian Distribution?"}
{"completion": " The Latex Code for equation Exponential Distributionis <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>", "tag": "Math,Statistics", "prompt": "Please give me some hints on equation Exponential Distribution?"}
{"completion": " The equation for Normal Gaussian Distribution is: <equation>X \\\\sim \\\\mathcal{N}(\\\\mu,\\\\sigma^2) \\\\\\\\ f(x)=\\\\frac{1}{\\\\sigma\\\\sqrt{2\\\\pi}}\\\\exp{[-\\\\frac{(x-\\\\mu)^{2}}{2\\\\sigma^{2}}]}</equation>. Here is the brief introduction of Normal Gaussian Distribution:\n        X denotes the random variable which follows the normal distribution. \\mu denotes the mean value and \\sigma denotes the standard deviation.\n    ", "tag": "Math,Statistics", "prompt": "I am interested in Normal Gaussian Distribution?"}
{"completion": " The Latex Code for equation Gamma Distributionis <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>", "tag": "Math,Statistics", "prompt": "Show me the latex code of equation Gamma Distribution?"}
{"completion": " The Latex Code for equation Binomial Distributionis <equation>X \\\\sim B(n,p) \\\\\\\\f(x)=\\\\begin{pmatrix}n\\\\\\\\ x\\\\end{pmatrix}p^{x}q^{n-x}=C^{k}_{n}p^{x}q^{n-x},q=1-p\\\\\\\\\\\\text{Binominal Mean}\\\\ \\\\mu=np\\\\\\\\\\\\text{Binominal Variance}\\\\ \\\\sigma^2=npq</equation>", "tag": "Math,Statistics", "prompt": "What is the latex code of equation Binomial Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\Gamma(a)</equation> in Gamma Distribution is: Gamma function of a.", "tag": "Math,Statistics", "prompt": "What does the symbol mean <equation>\\Gamma(a)</equation> in Gamma Distribution?"}
{"completion": " The equation for Gamma Distribution is: <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. Here is the brief introduction of Gamma Distribution:\n        Latex code for Gamma Distribution. A gamma distribution is a general type of statistical distribution that is related to the beta distribution and arises naturally in processes for which the waiting times between Poisson distributed events are relevant. Gamma distributions have two free parameters, labeled alpha and theta. We now let W denote the waiting time until the a-th event occurs and find the distribution of W. We could represent the situation as follows:\n        \n: Gamma function of a\n: Gamma function parameter\n: PDF of gamma distributed random variable X.\n: Mean of Gamma Distribution\n: Variance of Gamma Distribution\n: Skewness of Gamma Distribution\n: Kurtosis of Gamma Distribution\n\n\nRelated Documents\n\nGamma Distribution\n15.4 - Gamma Distributions\n\nRelated Videos\n\n\n", "tag": "Math,Statistics", "prompt": "I am interested in Gamma Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>f(x, \\lambda)=\\lambda e^{-\\lambda x}</equation> in Exponential Distribution is: PDF of Exponential Distribution.", "tag": "Math,Statistics", "prompt": "Can you explain the symbol <equation>f(x, \\lambda)=\\lambda e^{-\\lambda x}</equation> in Exponential Distribution?"}
{"completion": " The equation for Fisher Skewness is: <equation>\\\\gamma_1 = \\\\frac{{\\\\mu_3 }}{{\\\\mu_2 ^{{3 \\\\mathord{\\\\left/ {\\\\vphantom {3 2}} \\\\right. \\\\kern-\\\\nulldelimiterspace} 2}} }} = \\\\frac{{\\\\mu_3 }}{{\\\\sigma ^3 }}</equation>. Here is the brief introduction of Fisher Skewness:\n        Latex code for Fisher Skewness. \n        \n\n\nRelated Documents\n\nGamma Distribution\n\nRelated Videos\n\n\n", "tag": "Math,Statistics", "prompt": "I am interested in Fisher Skewness?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\gamma_{1} = \\frac{2}{\\sqrt{\\alpha}}</equation> in Gamma Distribution is: Skewness of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "Can you explain the symbol <equation>\\gamma_{1} = \\frac{2}{\\sqrt{\\alpha}}</equation> in Gamma Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>F(x, \\lambda)=1 - e^{-\\lambda x}</equation> in Exponential Distribution is: CDF of Exponential Distribution.", "tag": "Math,Statistics", "prompt": "What is the meaning of <equation>F(x, \\lambda)=1 - e^{-\\lambda x}</equation> in Exponential Distribution?"}
{"completion": " The Latex Code for equation Fisher Skewnessis <equation>\\\\gamma_1 = \\\\frac{{\\\\mu_3 }}{{\\\\mu_2 ^{{3 \\\\mathord{\\\\left/ {\\\\vphantom {3 2}} \\\\right. \\\\kern-\\\\nulldelimiterspace} 2}} }} = \\\\frac{{\\\\mu_3 }}{{\\\\sigma ^3 }}</equation>", "tag": "Math,Statistics", "prompt": "What is the equation of Fisher Skewness?"}
{"completion": " The Latex Code for equation Fisher Skewnessis <equation>\\\\gamma_1 = \\\\frac{{\\\\mu_3 }}{{\\\\mu_2 ^{{3 \\\\mathord{\\\\left/ {\\\\vphantom {3 2}} \\\\right. \\\\kern-\\\\nulldelimiterspace} 2}} }} = \\\\frac{{\\\\mu_3 }}{{\\\\sigma ^3 }}</equation>", "tag": "Math,Statistics", "prompt": "What is the latex code of equation Fisher Skewness?"}
{"completion": " The equation for Gamma Distribution is: <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. Here is the brief introduction of Gamma Distribution:\n        Latex code for Gamma Distribution. A gamma distribution is a general type of statistical distribution that is related to the beta distribution and arises naturally in processes for which the waiting times between Poisson distributed events are relevant. Gamma distributions have two free parameters, labeled alpha and theta. We now let W denote the waiting time until the a-th event occurs and find the distribution of W. We could represent the situation as follows:\n        \n: Gamma function of a\n: Gamma function parameter\n: PDF of gamma distributed random variable X.\n: Mean of Gamma Distribution\n: Variance of Gamma Distribution\n: Skewness of Gamma Distribution\n: Kurtosis of Gamma Distribution\n\n\nRelated Documents\n\nGamma Distribution\n15.4 - Gamma Distributions\n\nRelated Videos\n\n\n", "tag": "Math,Statistics", "prompt": "Can you give me a brief introduction to Gamma Distribution?"}
{"completion": " The equation for Poisson Distribution is: <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\ \\\\text{Poisson Variance} \\\\sigma^2=\\\\mu</equation>. Here is the brief introduction of Poisson Distribution:", "tag": "poisson,statistics", "prompt": "Can you explain Poisson Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>f(x, \\lambda)=\\lambda e^{-\\lambda x}</equation> in Exponential Distribution is: PDF of Exponential Distribution.", "tag": "Math,Statistics", "prompt": "What is the meaning of <equation>f(x, \\lambda)=\\lambda e^{-\\lambda x}</equation> in Exponential Distribution?"}
{"completion": " The equation for Binomial Distribution is: <equation>X \\\\sim B(n,p) \\\\\\\\f(x)=\\\\begin{pmatrix}n\\\\\\\\ x\\\\end{pmatrix}p^{x}q^{n-x}=C^{k}_{n}p^{x}q^{n-x},q=1-p\\\\\\\\\\\\text{Binominal Mean}\\\\ \\\\mu=np\\\\\\\\\\\\text{Binominal Variance}\\\\ \\\\sigma^2=npq</equation>. Here is the brief introduction of Binomial Distribution:\n        The binomial distribution measures in total n independent trials, the probability that x trials in total n trials are positive (like the getting positive of flipping a coin). In this formulation, f(x) denotes the probability that x positive trials are observed in n independent trials. p denote the probability that positive is observed in each single trial. q denotes the negative is observed, which equals to 1-p. \n    ", "tag": "Math,Statistics", "prompt": "Can you explain Binomial Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\gamma_{1} = \\frac{2}{\\sqrt{\\alpha}}</equation> in Gamma Distribution is: Skewness of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "What is the meaning of the symbol <equation>\\gamma_{1} = \\frac{2}{\\sqrt{\\alpha}}</equation> in Gamma Distribution?"}
{"completion": " The Latex Code for equation Normal Gaussian Distributionis <equation>X \\\\sim \\\\mathcal{N}(\\\\mu,\\\\sigma^2) \\\\\\\\ f(x)=\\\\frac{1}{\\\\sigma\\\\sqrt{2\\\\pi}}\\\\exp{[-\\\\frac{(x-\\\\mu)^{2}}{2\\\\sigma^{2}}]}</equation>", "tag": "Math,Statistics", "prompt": "Show me the latex code of equation Normal Gaussian Distribution?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean}\\\\ \\\\mu \\\\\\\\ \\\\text{Poisson Variance}\\\\ \\\\sigma^2=\\\\mu</equation>", "tag": "poisson,statistics", "prompt": "Show me the latex code of equation Poisson Distribution?"}
{"completion": " The equation for Binomial Distribution is: <equation>X \\\\sim B(n,p) \\\\\\\\f(x)=\\\\begin{pmatrix}n\\\\\\\\ x\\\\end{pmatrix}p^{x}q^{n-x}=C^{k}_{n}p^{x}q^{n-x},q=1-p\\\\\\\\\\\\text{Binominal Mean}\\\\ \\\\mu=np\\\\\\\\\\\\text{Binominal Variance}\\\\ \\\\sigma^2=npq</equation>. Here is the brief introduction of Binomial Distribution:\n        The binomial distribution measures in total n independent trials, the probability that x trials in total n trials are positive (like the getting positive of flipping a coin). In this formulation, f(x) denotes the probability that x positive trials are observed in n independent trials. p denote the probability that positive is observed in each single trial. q denotes the negative is observed, which equals to 1-p. \n    ", "tag": "Math,Statistics", "prompt": "Can you give me a brief introduction to Binomial Distribution?"}
{"completion": " The equation for Poisson Distribution is: <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\  \\\\text{Poisson Variance}\\\\sigma^2=\\\\mu</equation>. Here is the brief introduction of Poisson Distribution:\n        \\mu equals to the probability that an event occurs in a unit time period.\n    ", "tag": "Math,Statistics", "prompt": "What's the meaning of Poisson Distribution?"}
{"completion": " The related materials of Poisson Distribution is: ", "tag": "poisson,statistics", "prompt": "Can you help me find related materials of Poisson Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\gamma_{1} = \\frac{2}{\\sqrt{\\alpha}}</equation> in Gamma Distribution is: Skewness of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "Help me find the meaning of symbol <equation>\\gamma_{1} = \\frac{2}{\\sqrt{\\alpha}}</equation> in Gamma Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\alpha</equation> in Gamma Distribution is: Gamma function parameter.", "tag": "Math,Statistics", "prompt": "Can you explain the symbol <equation>\\alpha</equation> in Gamma Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>P(x) = \\frac{x^{\\alpha-1} e^{-frac{x}{\\theta}}}{\\Gamma(\\alpha) \\theta^{\\alpha}}</equation> in Gamma Distribution is: PDF of gamma distributed random variable X..", "tag": "Math,Statistics", "prompt": "Help me find the meaning of symbol <equation>P(x) = \\frac{x^{\\alpha-1} e^{-frac{x}{\\theta}}}{\\Gamma(\\alpha) \\theta^{\\alpha}}</equation> in Gamma Distribution?"}
{"completion": " The Latex Code for equation Fisher Skewnessis <equation>\\\\gamma_1 = \\\\frac{{\\\\mu_3 }}{{\\\\mu_2 ^{{3 \\\\mathord{\\\\left/ {\\\\vphantom {3 2}} \\\\right. \\\\kern-\\\\nulldelimiterspace} 2}} }} = \\\\frac{{\\\\mu_3 }}{{\\\\sigma ^3 }}</equation>", "tag": "Math,Statistics", "prompt": "Show me the latex code of equation Fisher Skewness?"}
{"completion": " The equation for Exponential Distribution is: <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. Here is the brief introduction of Exponential Distribution:\n\n: The rate parameter\n: Constant Exponential Parameter\n: PDF of Exponential Distribution\n: CDF of Exponential Distribution\n\n", "tag": "Math,Statistics", "prompt": "Can you explain Exponential Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\sigma^{2} = \\alpha \\theta^{2}</equation> in Gamma Distribution is: Variance of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "Can you explain the symbol <equation>\\sigma^{2} = \\alpha \\theta^{2}</equation> in Gamma Distribution?"}
{"completion": " The Latex Code for equation Exponential Distributionis <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>", "tag": "Math,Statistics", "prompt": "How to write equation Exponential Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\gamma_{1} = \\frac{2}{\\sqrt{\\alpha}}</equation> in Gamma Distribution is: Skewness of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "What is the meaning of <equation>\\gamma_{1} = \\frac{2}{\\sqrt{\\alpha}}</equation> in Gamma Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\alpha</equation> in Gamma Distribution is: Gamma function parameter.", "tag": "Math,Statistics", "prompt": "What does the symbol mean <equation>\\alpha</equation> in Gamma Distribution?"}
{"completion": " The equation for Binomial Distribution is: <equation>X \\\\sim B(n,p) \\\\\\\\f(x)=\\\\begin{pmatrix}n\\\\\\\\ x\\\\end{pmatrix}p^{x}q^{n-x}=C^{k}_{n}p^{x}q^{n-x},q=1-p\\\\\\\\\\\\text{Binominal Mean}\\\\ \\\\mu=np\\\\\\\\\\\\text{Binominal Variance}\\\\ \\\\sigma^2=npq</equation>. Here is the brief introduction of Binomial Distribution:\n        The binomial distribution measures in total n independent trials, the probability that x trials in total n trials are positive (like the getting positive of flipping a coin). In this formulation, f(x) denotes the probability that x positive trials are observed in n independent trials. p denote the probability that positive is observed in each single trial. q denotes the negative is observed, which equals to 1-p. \n    ", "tag": "Math,Statistics", "prompt": "I am interested in Binomial Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>P(x) = \\frac{x^{\\alpha-1} e^{-frac{x}{\\theta}}}{\\Gamma(\\alpha) \\theta^{\\alpha}}</equation> in Gamma Distribution is: PDF of gamma distributed random variable X..", "tag": "Math,Statistics", "prompt": "What does the symbol mean <equation>P(x) = \\frac{x^{\\alpha-1} e^{-frac{x}{\\theta}}}{\\Gamma(\\alpha) \\theta^{\\alpha}}</equation> in Gamma Distribution?"}
{"completion": " The equation for Poisson Distribution is: <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\  \\\\text{Poisson Variance}\\\\sigma^2=\\\\mu</equation>. Here is the brief introduction of Poisson Distribution:\n        \\mu equals to the probability that an event occurs in a unit time period.\n    ", "tag": "Math,Statistics", "prompt": "I am interested in Poisson Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>\\lambda=\\frac{1}{\\mu}</equation> in Exponential Distribution is: The rate parameter.", "tag": "Math,Statistics", "prompt": "Can you explain the symbol <equation>\\lambda=\\frac{1}{\\mu}</equation> in Exponential Distribution?"}
{"completion": " The equation for Binomial Distribution is: <equation>X \\\\sim B(n,p) \\\\\\\\f(x)=\\\\begin{pmatrix}n\\\\\\\\ x\\\\end{pmatrix}p^{x}q^{n-x}=C^{k}_{n}p^{x}q^{n-x},q=1-p\\\\\\\\\\\\text{Binominal Mean}\\\\ \\\\mu=np\\\\\\\\\\\\text{Binominal Variance}\\\\ \\\\sigma^2=npq</equation>. Here is the brief introduction of Binomial Distribution:\n        The binomial distribution measures in total n independent trials, the probability that x trials in total n trials are positive (like the getting positive of flipping a coin). In this formulation, f(x) denotes the probability that x positive trials are observed in n independent trials. p denote the probability that positive is observed in each single trial. q denotes the negative is observed, which equals to 1-p. \n    ", "tag": "Math,Statistics", "prompt": "What's the meaning of Binomial Distribution?"}
{"completion": " The Latex Code for equation Binomial Distributionis <equation>X \\\\sim B(n,p) \\\\\\\\f(x)=\\\\begin{pmatrix}n\\\\\\\\ x\\\\end{pmatrix}p^{x}q^{n-x}=C^{k}_{n}p^{x}q^{n-x},q=1-p\\\\\\\\\\\\text{Binominal Mean}\\\\ \\\\mu=np\\\\\\\\\\\\text{Binominal Variance}\\\\ \\\\sigma^2=npq</equation>", "tag": "Math,Statistics", "prompt": "How to write equation Binomial Distribution?"}
{"completion": " The equation for Gamma Distribution is: <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. Here is the brief introduction of Gamma Distribution:\n        Latex code for Gamma Distribution. A gamma distribution is a general type of statistical distribution that is related to the beta distribution and arises naturally in processes for which the waiting times between Poisson distributed events are relevant. Gamma distributions have two free parameters, labeled alpha and theta. We now let W denote the waiting time until the a-th event occurs and find the distribution of W. We could represent the situation as follows:\n        \n: Gamma function of a\n: Gamma function parameter\n: PDF of gamma distributed random variable X.\n: Mean of Gamma Distribution\n: Variance of Gamma Distribution\n: Skewness of Gamma Distribution\n: Kurtosis of Gamma Distribution\n\n\nRelated Documents\n\nGamma Distribution\n15.4 - Gamma Distributions\n\nRelated Videos\n\n\n", "tag": "Math,Statistics", "prompt": "Can you explain Gamma Distribution?"}
{"completion": " The equation for Fisher Skewness is: <equation>\\\\gamma_1 = \\\\frac{{\\\\mu_3 }}{{\\\\mu_2 ^{{3 \\\\mathord{\\\\left/ {\\\\vphantom {3 2}} \\\\right. \\\\kern-\\\\nulldelimiterspace} 2}} }} = \\\\frac{{\\\\mu_3 }}{{\\\\sigma ^3 }}</equation>. Here is the brief introduction of Fisher Skewness:\n        Latex code for Fisher Skewness. \n        \n\n\nRelated Documents\n\nGamma Distribution\n\nRelated Videos\n\n\n", "tag": "Math,Statistics", "prompt": "Can you give me a brief introduction to Fisher Skewness?"}
{"completion": " The Latex Code for equation Gamma Distributionis <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>", "tag": "Math,Statistics", "prompt": "What is the latex code of equation Gamma Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>F(x, \\lambda)=1 - e^{-\\lambda x}</equation> in Exponential Distribution is: CDF of Exponential Distribution.", "tag": "Math,Statistics", "prompt": "What does the symbol mean <equation>F(x, \\lambda)=1 - e^{-\\lambda x}</equation> in Exponential Distribution?"}
{"completion": " The Latex Code for equation Fisher Skewnessis <equation>\\\\gamma_1 = \\\\frac{{\\\\mu_3 }}{{\\\\mu_2 ^{{3 \\\\mathord{\\\\left/ {\\\\vphantom {3 2}} \\\\right. \\\\kern-\\\\nulldelimiterspace} 2}} }} = \\\\frac{{\\\\mu_3 }}{{\\\\sigma ^3 }}</equation>", "tag": "Math,Statistics", "prompt": "How to write equation Fisher Skewness?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\sigma^{2} = \\alpha \\theta^{2}</equation> in Gamma Distribution is: Variance of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "What is the meaning of <equation>\\sigma^{2} = \\alpha \\theta^{2}</equation> in Gamma Distribution?"}
{"completion": " The equation for Poisson Distribution is: <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean}\\\\ \\\\mu \\\\\\\\ \\\\text{Poisson Variance}\\\\ \\\\sigma^2=\\\\mu</equation>. Here is the brief introduction of Poisson Distribution:", "tag": "poisson,statistics", "prompt": "I am interested in Poisson Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\Gamma(a)</equation> in Gamma Distribution is: Gamma function of a.", "tag": "Math,Statistics", "prompt": "What is the meaning of the symbol <equation>\\Gamma(a)</equation> in Gamma Distribution?"}
{"completion": " The equation for Poisson Distribution is: <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean}\\\\ \\\\mu \\\\\\\\ \\\\text{Poisson Variance}\\\\ \\\\sigma^2=\\\\mu</equation>. Here is the brief introduction of Poisson Distribution:", "tag": "poisson,statistics", "prompt": "Please give me detailed tutorial of Poisson Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>e</equation> in Exponential Distribution is: Constant Exponential Parameter.", "tag": "Math,Statistics", "prompt": "Can you explain the symbol <equation>e</equation> in Exponential Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\mu = \\alpha \\theta</equation> in Gamma Distribution is: Mean of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "Can you explain the symbol <equation>\\mu = \\alpha \\theta</equation> in Gamma Distribution?"}
{"completion": " The Latex Code for equation Exponential Distributionis <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>", "tag": "Math,Statistics", "prompt": "What is the latex code of equation Exponential Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\gamma_{2} = \\frac{6}{\\alpha}</equation> in Gamma Distribution is: Kurtosis of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "What is the meaning of <equation>\\gamma_{2} = \\frac{6}{\\alpha}</equation> in Gamma Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\mu = \\alpha \\theta</equation> in Gamma Distribution is: Mean of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "What does the symbol mean <equation>\\mu = \\alpha \\theta</equation> in Gamma Distribution?"}
{"completion": " The equation for Exponential Distribution is: <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. Here is the brief introduction of Exponential Distribution:\n\n: The rate parameter\n: Constant Exponential Parameter\n: PDF of Exponential Distribution\n: CDF of Exponential Distribution\n\n", "tag": "Math,Statistics", "prompt": "Please give me detailed tutorial of Exponential Distribution?"}
{"completion": " The Latex Code for equation Normal Gaussian Distributionis <equation>X \\\\sim \\\\mathcal{N}(\\\\mu,\\\\sigma^2) \\\\\\\\ f(x)=\\\\frac{1}{\\\\sigma\\\\sqrt{2\\\\pi}}\\\\exp{[-\\\\frac{(x-\\\\mu)^{2}}{2\\\\sigma^{2}}]}</equation>", "tag": "Math,Statistics", "prompt": "How to write equation Normal Gaussian Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\gamma_{2} = \\frac{6}{\\alpha}</equation> in Gamma Distribution is: Kurtosis of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "Help me find the meaning of symbol <equation>\\gamma_{2} = \\frac{6}{\\alpha}</equation> in Gamma Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\alpha</equation> in Gamma Distribution is: Gamma function parameter.", "tag": "Math,Statistics", "prompt": "Help me find the meaning of symbol <equation>\\alpha</equation> in Gamma Distribution?"}
{"completion": " The Latex Code for equation Fisher Skewnessis <equation>\\\\gamma_1 = \\\\frac{{\\\\mu_3 }}{{\\\\mu_2 ^{{3 \\\\mathord{\\\\left/ {\\\\vphantom {3 2}} \\\\right. \\\\kern-\\\\nulldelimiterspace} 2}} }} = \\\\frac{{\\\\mu_3 }}{{\\\\sigma ^3 }}</equation>", "tag": "Math,Statistics", "prompt": "Please give me some hints on equation Fisher Skewness?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\gamma_{2} = \\frac{6}{\\alpha}</equation> in Gamma Distribution is: Kurtosis of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "What does the symbol mean <equation>\\gamma_{2} = \\frac{6}{\\alpha}</equation> in Gamma Distribution?"}
{"completion": " The Latex Code for equation Fisher Skewnessis <equation>\\\\gamma_1 = \\\\frac{{\\\\mu_3 }}{{\\\\mu_2 ^{{3 \\\\mathord{\\\\left/ {\\\\vphantom {3 2}} \\\\right. \\\\kern-\\\\nulldelimiterspace} 2}} }} = \\\\frac{{\\\\mu_3 }}{{\\\\sigma ^3 }}</equation>", "tag": "Math,Statistics", "prompt": "Can you write equation Fisher Skewness?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\  \\\\text{Poisson Variance}\\\\sigma^2=\\\\mu</equation>", "tag": "Math,Statistics", "prompt": "Show me the latex code of equation Poisson Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>e</equation> in Exponential Distribution is: Constant Exponential Parameter.", "tag": "Math,Statistics", "prompt": "What is the meaning of the symbol <equation>e</equation> in Exponential Distribution?"}
{"completion": " The equation for Poisson Distribution is: <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\ \\\\text{Poisson Variance} \\\\sigma^2=\\\\mu</equation>. Here is the brief introduction of Poisson Distribution:", "tag": "poisson,statistics", "prompt": "I am interested in Poisson Distribution?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\ \\\\text{Poisson Variance} \\\\sigma^2=\\\\mu</equation>", "tag": "poisson,statistics", "prompt": "Please give me some hints on equation Poisson Distribution?"}
{"completion": " The Latex Code for equation Gamma Distributionis <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>", "tag": "Math,Statistics", "prompt": "Please give me some hints on equation Gamma Distribution?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\  \\\\text{Poisson Variance}\\\\sigma^2=\\\\mu</equation>", "tag": "Math,Statistics", "prompt": "What is the equation of Poisson Distribution?"}
{"completion": " The equation for Fisher Skewness is: <equation>\\\\gamma_1 = \\\\frac{{\\\\mu_3 }}{{\\\\mu_2 ^{{3 \\\\mathord{\\\\left/ {\\\\vphantom {3 2}} \\\\right. \\\\kern-\\\\nulldelimiterspace} 2}} }} = \\\\frac{{\\\\mu_3 }}{{\\\\sigma ^3 }}</equation>. Here is the brief introduction of Fisher Skewness:\n        Latex code for Fisher Skewness. \n        \n\n\nRelated Documents\n\nGamma Distribution\n\nRelated Videos\n\n\n", "tag": "Math,Statistics", "prompt": "What's the meaning of Fisher Skewness?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>\\lambda=\\frac{1}{\\mu}</equation> in Exponential Distribution is: The rate parameter.", "tag": "Math,Statistics", "prompt": "What is the meaning of the symbol <equation>\\lambda=\\frac{1}{\\mu}</equation> in Exponential Distribution?"}
{"completion": " The related materials of Poisson Distribution is: ", "tag": "Math,Statistics", "prompt": "Can you help me find related materials of Poisson Distribution?"}
{"completion": " The Latex Code for equation Normal Gaussian Distributionis <equation>X \\\\sim \\\\mathcal{N}(\\\\mu,\\\\sigma^2) \\\\\\\\ f(x)=\\\\frac{1}{\\\\sigma\\\\sqrt{2\\\\pi}}\\\\exp{[-\\\\frac{(x-\\\\mu)^{2}}{2\\\\sigma^{2}}]}</equation>", "tag": "Math,Statistics", "prompt": "What is the latex code of equation Normal Gaussian Distribution?"}
{"completion": " The equation for Poisson Distribution is: <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\ \\\\text{Poisson Variance} \\\\sigma^2=\\\\mu</equation>. Here is the brief introduction of Poisson Distribution:", "tag": "poisson,statistics", "prompt": "What's the meaning of Poisson Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\sigma^{2} = \\alpha \\theta^{2}</equation> in Gamma Distribution is: Variance of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "What does the symbol mean <equation>\\sigma^{2} = \\alpha \\theta^{2}</equation> in Gamma Distribution?"}
{"completion": " The Latex Code for equation Normal Gaussian Distributionis <equation>X \\\\sim \\\\mathcal{N}(\\\\mu,\\\\sigma^2) \\\\\\\\ f(x)=\\\\frac{1}{\\\\sigma\\\\sqrt{2\\\\pi}}\\\\exp{[-\\\\frac{(x-\\\\mu)^{2}}{2\\\\sigma^{2}}]}</equation>", "tag": "Math,Statistics", "prompt": "Please give me some hints on equation Normal Gaussian Distribution?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\  \\\\text{Poisson Variance}\\\\sigma^2=\\\\mu</equation>", "tag": "Math,Statistics", "prompt": "What is the latex code of equation Poisson Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>P(x) = \\frac{x^{\\alpha-1} e^{-frac{x}{\\theta}}}{\\Gamma(\\alpha) \\theta^{\\alpha}}</equation> in Gamma Distribution is: PDF of gamma distributed random variable X..", "tag": "Math,Statistics", "prompt": "What is the meaning of the symbol <equation>P(x) = \\frac{x^{\\alpha-1} e^{-frac{x}{\\theta}}}{\\Gamma(\\alpha) \\theta^{\\alpha}}</equation> in Gamma Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\sigma^{2} = \\alpha \\theta^{2}</equation> in Gamma Distribution is: Variance of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "Help me find the meaning of symbol <equation>\\sigma^{2} = \\alpha \\theta^{2}</equation> in Gamma Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>P(x) = \\frac{x^{\\alpha-1} e^{-frac{x}{\\theta}}}{\\Gamma(\\alpha) \\theta^{\\alpha}}</equation> in Gamma Distribution is: PDF of gamma distributed random variable X..", "tag": "Math,Statistics", "prompt": "Can you explain the symbol <equation>P(x) = \\frac{x^{\\alpha-1} e^{-frac{x}{\\theta}}}{\\Gamma(\\alpha) \\theta^{\\alpha}}</equation> in Gamma Distribution?"}
{"completion": " The Latex Code for equation Binomial Distributionis <equation>X \\\\sim B(n,p) \\\\\\\\f(x)=\\\\begin{pmatrix}n\\\\\\\\ x\\\\end{pmatrix}p^{x}q^{n-x}=C^{k}_{n}p^{x}q^{n-x},q=1-p\\\\\\\\\\\\text{Binominal Mean}\\\\ \\\\mu=np\\\\\\\\\\\\text{Binominal Variance}\\\\ \\\\sigma^2=npq</equation>", "tag": "Math,Statistics", "prompt": "Show me the latex code of equation Binomial Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\mu = \\alpha \\theta</equation> in Gamma Distribution is: Mean of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "What is the meaning of <equation>\\mu = \\alpha \\theta</equation> in Gamma Distribution?"}
{"completion": " The related materials of Binomial Distribution is: ", "tag": "Math,Statistics", "prompt": "Can you help me find related materials of Binomial Distribution?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\ \\\\text{Poisson Variance} \\\\sigma^2=\\\\mu</equation>", "tag": "poisson,statistics", "prompt": "Show me the latex code of equation Poisson Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\gamma_{1} = \\frac{2}{\\sqrt{\\alpha}}</equation> in Gamma Distribution is: Skewness of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "What does the symbol mean <equation>\\gamma_{1} = \\frac{2}{\\sqrt{\\alpha}}</equation> in Gamma Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>F(x, \\lambda)=1 - e^{-\\lambda x}</equation> in Exponential Distribution is: CDF of Exponential Distribution.", "tag": "Math,Statistics", "prompt": "What is the meaning of the symbol <equation>F(x, \\lambda)=1 - e^{-\\lambda x}</equation> in Exponential Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>P(x) = \\frac{x^{\\alpha-1} e^{-frac{x}{\\theta}}}{\\Gamma(\\alpha) \\theta^{\\alpha}}</equation> in Gamma Distribution is: PDF of gamma distributed random variable X..", "tag": "Math,Statistics", "prompt": "What is the meaning of <equation>P(x) = \\frac{x^{\\alpha-1} e^{-frac{x}{\\theta}}}{\\Gamma(\\alpha) \\theta^{\\alpha}}</equation> in Gamma Distribution?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\  \\\\text{Poisson Variance}\\\\sigma^2=\\\\mu</equation>", "tag": "Math,Statistics", "prompt": "How to write equation Poisson Distribution?"}
{"completion": " The Latex Code for equation Gamma Distributionis <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>", "tag": "Math,Statistics", "prompt": "How to write equation Gamma Distribution?"}
{"completion": " The equation for Poisson Distribution is: <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\  \\\\text{Poisson Variance}\\\\sigma^2=\\\\mu</equation>. Here is the brief introduction of Poisson Distribution:\n        \\mu equals to the probability that an event occurs in a unit time period.\n    ", "tag": "Math,Statistics", "prompt": "Can you explain Poisson Distribution?"}
{"completion": " The equation for Poisson Distribution is: <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\ \\\\text{Poisson Variance} \\\\sigma^2=\\\\mu</equation>. Here is the brief introduction of Poisson Distribution:", "tag": "poisson,statistics", "prompt": "Please give me detailed tutorial of Poisson Distribution?"}
{"completion": " The related materials of Normal Gaussian Distribution is: ", "tag": "Math,Statistics", "prompt": "Can you help me find related materials of Normal Gaussian Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>e</equation> in Exponential Distribution is: Constant Exponential Parameter.", "tag": "Math,Statistics", "prompt": "Help me find the meaning of symbol <equation>e</equation> in Exponential Distribution?"}
{"completion": " The equation for Poisson Distribution is: <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\ \\\\text{Poisson Variance} \\\\sigma^2=\\\\mu</equation>. Here is the brief introduction of Poisson Distribution:", "tag": "poisson,statistics", "prompt": "Can you give me a brief introduction to Poisson Distribution?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\ \\\\text{Poisson Variance} \\\\sigma^2=\\\\mu</equation>", "tag": "poisson,statistics", "prompt": "What is the latex code of equation Poisson Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>F(x, \\lambda)=1 - e^{-\\lambda x}</equation> in Exponential Distribution is: CDF of Exponential Distribution.", "tag": "Math,Statistics", "prompt": "Help me find the meaning of symbol <equation>F(x, \\lambda)=1 - e^{-\\lambda x}</equation> in Exponential Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\Gamma(a)</equation> in Gamma Distribution is: Gamma function of a.", "tag": "Math,Statistics", "prompt": "Help me find the meaning of symbol <equation>\\Gamma(a)</equation> in Gamma Distribution?"}
{"completion": " The Latex Code for equation Binomial Distributionis <equation>X \\\\sim B(n,p) \\\\\\\\f(x)=\\\\begin{pmatrix}n\\\\\\\\ x\\\\end{pmatrix}p^{x}q^{n-x}=C^{k}_{n}p^{x}q^{n-x},q=1-p\\\\\\\\\\\\text{Binominal Mean}\\\\ \\\\mu=np\\\\\\\\\\\\text{Binominal Variance}\\\\ \\\\sigma^2=npq</equation>", "tag": "Math,Statistics", "prompt": "Can you write equation Binomial Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\mu = \\alpha \\theta</equation> in Gamma Distribution is: Mean of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "Help me find the meaning of symbol <equation>\\mu = \\alpha \\theta</equation> in Gamma Distribution?"}
{"completion": " The equation for Gamma Distribution is: <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. Here is the brief introduction of Gamma Distribution:\n        Latex code for Gamma Distribution. A gamma distribution is a general type of statistical distribution that is related to the beta distribution and arises naturally in processes for which the waiting times between Poisson distributed events are relevant. Gamma distributions have two free parameters, labeled alpha and theta. We now let W denote the waiting time until the a-th event occurs and find the distribution of W. We could represent the situation as follows:\n        \n: Gamma function of a\n: Gamma function parameter\n: PDF of gamma distributed random variable X.\n: Mean of Gamma Distribution\n: Variance of Gamma Distribution\n: Skewness of Gamma Distribution\n: Kurtosis of Gamma Distribution\n\n\nRelated Documents\n\nGamma Distribution\n15.4 - Gamma Distributions\n\nRelated Videos\n\n\n", "tag": "Math,Statistics", "prompt": "What's the meaning of Gamma Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>\\lambda=\\frac{1}{\\mu}</equation> in Exponential Distribution is: The rate parameter.", "tag": "Math,Statistics", "prompt": "Help me find the meaning of symbol <equation>\\lambda=\\frac{1}{\\mu}</equation> in Exponential Distribution?"}
{"completion": " The equation for Fisher Skewness is: <equation>\\\\gamma_1 = \\\\frac{{\\\\mu_3 }}{{\\\\mu_2 ^{{3 \\\\mathord{\\\\left/ {\\\\vphantom {3 2}} \\\\right. \\\\kern-\\\\nulldelimiterspace} 2}} }} = \\\\frac{{\\\\mu_3 }}{{\\\\sigma ^3 }}</equation>. Here is the brief introduction of Fisher Skewness:\n        Latex code for Fisher Skewness. \n        \n\n\nRelated Documents\n\nGamma Distribution\n\nRelated Videos\n\n\n", "tag": "Math,Statistics", "prompt": "Can you explain Fisher Skewness?"}
{"completion": " The Latex Code for equation Gamma Distributionis <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>", "tag": "Math,Statistics", "prompt": "What is the equation of Gamma Distribution?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\  \\\\text{Poisson Variance}\\\\sigma^2=\\\\mu</equation>", "tag": "Math,Statistics", "prompt": "Please give me some hints on equation Poisson Distribution?"}
{"completion": " The equation for Normal Gaussian Distribution is: <equation>X \\\\sim \\\\mathcal{N}(\\\\mu,\\\\sigma^2) \\\\\\\\ f(x)=\\\\frac{1}{\\\\sigma\\\\sqrt{2\\\\pi}}\\\\exp{[-\\\\frac{(x-\\\\mu)^{2}}{2\\\\sigma^{2}}]}</equation>. Here is the brief introduction of Normal Gaussian Distribution:\n        X denotes the random variable which follows the normal distribution. \\mu denotes the mean value and \\sigma denotes the standard deviation.\n    ", "tag": "Math,Statistics", "prompt": "Please give me detailed tutorial of Normal Gaussian Distribution?"}
{"completion": " The related materials of Gamma Distribution is: 1.Gamma Distribution:<url>https://mathworld.wolfram.com/GammaDistribution.html</url>;2.15.4 - Gamma Distributions:<url>https://online.stat.psu.edu/stat414/lesson/15/15.4</url>;", "tag": "Math,Statistics", "prompt": "Can you help me find related materials of Gamma Distribution?"}
{"completion": " The equation for Gamma Distribution is: <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. Here is the brief introduction of Gamma Distribution:\n        Latex code for Gamma Distribution. A gamma distribution is a general type of statistical distribution that is related to the beta distribution and arises naturally in processes for which the waiting times between Poisson distributed events are relevant. Gamma distributions have two free parameters, labeled alpha and theta. We now let W denote the waiting time until the a-th event occurs and find the distribution of W. We could represent the situation as follows:\n        \n: Gamma function of a\n: Gamma function parameter\n: PDF of gamma distributed random variable X.\n: Mean of Gamma Distribution\n: Variance of Gamma Distribution\n: Skewness of Gamma Distribution\n: Kurtosis of Gamma Distribution\n\n\nRelated Documents\n\nGamma Distribution\n15.4 - Gamma Distributions\n\nRelated Videos\n\n\n", "tag": "Math,Statistics", "prompt": "Please give me detailed tutorial of Gamma Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\mu = \\alpha \\theta</equation> in Gamma Distribution is: Mean of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "What is the meaning of the symbol <equation>\\mu = \\alpha \\theta</equation> in Gamma Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\Gamma(a)</equation> in Gamma Distribution is: Gamma function of a.", "tag": "Math,Statistics", "prompt": "Can you explain the symbol <equation>\\Gamma(a)</equation> in Gamma Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>\\lambda=\\frac{1}{\\mu}</equation> in Exponential Distribution is: The rate parameter.", "tag": "Math,Statistics", "prompt": "What does the symbol mean <equation>\\lambda=\\frac{1}{\\mu}</equation> in Exponential Distribution?"}
{"completion": " The equation for Fisher Skewness is: <equation>\\\\gamma_1 = \\\\frac{{\\\\mu_3 }}{{\\\\mu_2 ^{{3 \\\\mathord{\\\\left/ {\\\\vphantom {3 2}} \\\\right. \\\\kern-\\\\nulldelimiterspace} 2}} }} = \\\\frac{{\\\\mu_3 }}{{\\\\sigma ^3 }}</equation>. Here is the brief introduction of Fisher Skewness:\n        Latex code for Fisher Skewness. \n        \n\n\nRelated Documents\n\nGamma Distribution\n\nRelated Videos\n\n\n", "tag": "Math,Statistics", "prompt": "Please give me detailed tutorial of Fisher Skewness?"}
{"completion": " The related materials of Fisher Skewness is: 1.Gamma Distribution:<url>https://mathworld.wolfram.com/GammaDistribution.html</url>;", "tag": "Math,Statistics", "prompt": "Can you help me find related materials of Fisher Skewness?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\gamma_{2} = \\frac{6}{\\alpha}</equation> in Gamma Distribution is: Kurtosis of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "Can you explain the symbol <equation>\\gamma_{2} = \\frac{6}{\\alpha}</equation> in Gamma Distribution?"}
{"completion": " The equation for Binomial Distribution is: <equation>X \\\\sim B(n,p) \\\\\\\\f(x)=\\\\begin{pmatrix}n\\\\\\\\ x\\\\end{pmatrix}p^{x}q^{n-x}=C^{k}_{n}p^{x}q^{n-x},q=1-p\\\\\\\\\\\\text{Binominal Mean}\\\\ \\\\mu=np\\\\\\\\\\\\text{Binominal Variance}\\\\ \\\\sigma^2=npq</equation>. Here is the brief introduction of Binomial Distribution:\n        The binomial distribution measures in total n independent trials, the probability that x trials in total n trials are positive (like the getting positive of flipping a coin). In this formulation, f(x) denotes the probability that x positive trials are observed in n independent trials. p denote the probability that positive is observed in each single trial. q denotes the negative is observed, which equals to 1-p. \n    ", "tag": "Math,Statistics", "prompt": "Please give me detailed tutorial of Binomial Distribution?"}
{"completion": " The equation for Exponential Distribution is: <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. Here is the brief introduction of Exponential Distribution:\n\n: The rate parameter\n: Constant Exponential Parameter\n: PDF of Exponential Distribution\n: CDF of Exponential Distribution\n\n", "tag": "Math,Statistics", "prompt": "Can you give me a brief introduction to Exponential Distribution?"}
{"completion": " The Latex Code for equation Exponential Distributionis <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>", "tag": "Math,Statistics", "prompt": "Can you write equation Exponential Distribution?"}
{"completion": " The Latex Code for equation Gamma Distributionis <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>", "tag": "Math,Statistics", "prompt": "Can you write equation Gamma Distribution?"}
{"completion": " The related materials of Exponential Distribution is: ", "tag": "Math,Statistics", "prompt": "Can you help me find related materials of Exponential Distribution?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean}\\\\ \\\\mu \\\\\\\\ \\\\text{Poisson Variance}\\\\ \\\\sigma^2=\\\\mu</equation>", "tag": "poisson,statistics", "prompt": "What is the latex code of equation Poisson Distribution?"}
{"completion": " The Latex Code for equation Binomial Distributionis <equation>X \\\\sim B(n,p) \\\\\\\\f(x)=\\\\begin{pmatrix}n\\\\\\\\ x\\\\end{pmatrix}p^{x}q^{n-x}=C^{k}_{n}p^{x}q^{n-x},q=1-p\\\\\\\\\\\\text{Binominal Mean}\\\\ \\\\mu=np\\\\\\\\\\\\text{Binominal Variance}\\\\ \\\\sigma^2=npq</equation>", "tag": "Math,Statistics", "prompt": "What is the equation of Binomial Distribution?"}
{"completion": " The equation for Poisson Distribution is: <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean}\\\\ \\\\mu \\\\\\\\ \\\\text{Poisson Variance}\\\\ \\\\sigma^2=\\\\mu</equation>. Here is the brief introduction of Poisson Distribution:", "tag": "poisson,statistics", "prompt": "What's the meaning of Poisson Distribution?"}
{"completion": " The Latex Code for equation Binomial Distributionis <equation>X \\\\sim B(n,p) \\\\\\\\f(x)=\\\\begin{pmatrix}n\\\\\\\\ x\\\\end{pmatrix}p^{x}q^{n-x}=C^{k}_{n}p^{x}q^{n-x},q=1-p\\\\\\\\\\\\text{Binominal Mean}\\\\ \\\\mu=np\\\\\\\\\\\\text{Binominal Variance}\\\\ \\\\sigma^2=npq</equation>", "tag": "Math,Statistics", "prompt": "Please give me some hints on equation Binomial Distribution?"}
{"completion": " The Latex Code for equation Exponential Distributionis <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>", "tag": "Math,Statistics", "prompt": "Show me the latex code of equation Exponential Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\gamma_{2} = \\frac{6}{\\alpha}</equation> in Gamma Distribution is: Kurtosis of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "What is the meaning of the symbol <equation>\\gamma_{2} = \\frac{6}{\\alpha}</equation> in Gamma Distribution?"}
{"completion": " The equation for Exponential Distribution is: <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. Here is the brief introduction of Exponential Distribution:\n\n: The rate parameter\n: Constant Exponential Parameter\n: PDF of Exponential Distribution\n: CDF of Exponential Distribution\n\n", "tag": "Math,Statistics", "prompt": "What's the meaning of Exponential Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\Gamma(a)</equation> in Gamma Distribution is: Gamma function of a.", "tag": "Math,Statistics", "prompt": "What is the meaning of <equation>\\Gamma(a)</equation> in Gamma Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>e</equation> in Exponential Distribution is: Constant Exponential Parameter.", "tag": "Math,Statistics", "prompt": "What does the symbol mean <equation>e</equation> in Exponential Distribution?"}
{"completion": " The related materials of Poisson Distribution is: ", "tag": "poisson,statistics", "prompt": "Can you help me find related materials of Poisson Distribution?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean}\\\\ \\\\mu \\\\\\\\ \\\\text{Poisson Variance}\\\\ \\\\sigma^2=\\\\mu</equation>", "tag": "poisson,statistics", "prompt": "What is the equation of Poisson Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>e</equation> in Exponential Distribution is: Constant Exponential Parameter.", "tag": "Math,Statistics", "prompt": "What is the meaning of <equation>e</equation> in Exponential Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\alpha</equation> in Gamma Distribution is: Gamma function parameter.", "tag": "Math,Statistics", "prompt": "What is the meaning of the symbol <equation>\\alpha</equation> in Gamma Distribution?"}
{"completion": " The equation for Poisson Distribution is: <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\  \\\\text{Poisson Variance}\\\\sigma^2=\\\\mu</equation>. Here is the brief introduction of Poisson Distribution:\n        \\mu equals to the probability that an event occurs in a unit time period.\n    ", "tag": "Math,Statistics", "prompt": "Please give me detailed tutorial of Poisson Distribution?"}
{"completion": " The equation for Exponential Distribution is: <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. Here is the brief introduction of Exponential Distribution:\n\n: The rate parameter\n: Constant Exponential Parameter\n: PDF of Exponential Distribution\n: CDF of Exponential Distribution\n\n", "tag": "Math,Statistics", "prompt": "I am interested in Exponential Distribution?"}
{"completion": " The equation for Exponential Distribution is <equation>f(x, \\\\lambda)=\\\\lambda e^{-\\\\lambda x} \\\\\\\\\\ F(x, \\\\lambda)=1 - e^{-\\\\lambda x}</equation>. The meaning of symbol <equation>f(x, \\lambda)=\\lambda e^{-\\lambda x}</equation> in Exponential Distribution is: PDF of Exponential Distribution.", "tag": "Math,Statistics", "prompt": "Help me find the meaning of symbol <equation>f(x, \\lambda)=\\lambda e^{-\\lambda x}</equation> in Exponential Distribution?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\  \\\\text{Poisson Variance}\\\\sigma^2=\\\\mu</equation>", "tag": "Math,Statistics", "prompt": "Can you write equation Poisson Distribution?"}
{"completion": " The Latex Code for equation Normal Gaussian Distributionis <equation>X \\\\sim \\\\mathcal{N}(\\\\mu,\\\\sigma^2) \\\\\\\\ f(x)=\\\\frac{1}{\\\\sigma\\\\sqrt{2\\\\pi}}\\\\exp{[-\\\\frac{(x-\\\\mu)^{2}}{2\\\\sigma^{2}}]}</equation>", "tag": "Math,Statistics", "prompt": "Can you write equation Normal Gaussian Distribution?"}
{"completion": " The equation for Poisson Distribution is: <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean}\\\\ \\\\mu \\\\\\\\ \\\\text{Poisson Variance}\\\\ \\\\sigma^2=\\\\mu</equation>. Here is the brief introduction of Poisson Distribution:", "tag": "poisson,statistics", "prompt": "Can you explain Poisson Distribution?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\ \\\\text{Poisson Variance} \\\\sigma^2=\\\\mu</equation>", "tag": "poisson,statistics", "prompt": "Can you write equation Poisson Distribution?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\ \\\\text{Poisson Variance} \\\\sigma^2=\\\\mu</equation>", "tag": "poisson,statistics", "prompt": "What is the equation of Poisson Distribution?"}
{"completion": " The equation for Normal Gaussian Distribution is: <equation>X \\\\sim \\\\mathcal{N}(\\\\mu,\\\\sigma^2) \\\\\\\\ f(x)=\\\\frac{1}{\\\\sigma\\\\sqrt{2\\\\pi}}\\\\exp{[-\\\\frac{(x-\\\\mu)^{2}}{2\\\\sigma^{2}}]}</equation>. Here is the brief introduction of Normal Gaussian Distribution:\n        X denotes the random variable which follows the normal distribution. \\mu denotes the mean value and \\sigma denotes the standard deviation.\n    ", "tag": "Math,Statistics", "prompt": "Can you give me a brief introduction to Normal Gaussian Distribution?"}
{"completion": " The Latex Code for equation Poisson Distributionis <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean}\\\\ \\\\mu \\\\\\\\ \\\\text{Poisson Variance}\\\\ \\\\sigma^2=\\\\mu</equation>", "tag": "poisson,statistics", "prompt": "How to write equation Poisson Distribution?"}
{"completion": " The equation for Poisson Distribution is: <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean}\\\\ \\\\mu \\\\\\\\ \\\\text{Poisson Variance}\\\\ \\\\sigma^2=\\\\mu</equation>. Here is the brief introduction of Poisson Distribution:", "tag": "poisson,statistics", "prompt": "Can you give me a brief introduction to Poisson Distribution?"}
{"completion": " The equation for Gamma Distribution is <equation>\\\\Gamma \\\\left( a \\\\right) = \\\\int\\\\limits_0^\\\\infty {s^{a - 1} } e^{ - s} ds \\\\\\\\\\             P(x) = \\\\frac{x^{\\\\alpha-1} e^{-frac{x}{\\\\theta}}}{\\\\Gamma(\\\\alpha) \\\\theta^{\\\\alpha}} \\\\\\\\\\             \\\\mu = \\\\alpha \\\\theta \\\\\\\\\\             \\\\sigma^{2} = \\\\alpha \\\\theta^{2} \\\\\\\\\\             \\\\gamma_{1} = \\\\frac{2}{\\\\sqrt{\\\\alpha}} \\\\\\\\\\             \\\\gamma_{2} = \\\\frac{6}{\\\\alpha}</equation>. The meaning of symbol <equation>\\sigma^{2} = \\alpha \\theta^{2}</equation> in Gamma Distribution is: Variance of Gamma Distribution.", "tag": "Math,Statistics", "prompt": "What is the meaning of the symbol <equation>\\sigma^{2} = \\alpha \\theta^{2}</equation> in Gamma Distribution?"}
{"completion": " The equation for Poisson Distribution is: <equation>X \\\\sim \\\\pi(\\\\mu) \\\\\\\\f(x)=\\\\frac{\\\\mu^{x}}{x!}e^{-\\\\mu}\\\\\\\\ \\\\text{Poisson Mean} \\\\mu \\\\\\\\  \\\\text{Poisson Variance}\\\\sigma^2=\\\\mu</equation>. Here is the brief introduction of Poisson Distribution:\n        \\mu equals to the probability that an event occurs in a unit time period.\n    ", "tag": "Math,Statistics", "prompt": "Can you give me a brief introduction to Poisson Distribution?"}