lecture_34

Wed Aug 1 09:07:09 CDT 2012

Examples of approximations:

[\sqrt{80} \approx \sqrt{82} \approx 9]

(

DNHI

An unfair coin with [P(H) = \frac{ 3}{ 5}] is tossed 100 times. What is the probability (approx.) of more than 64 heads?

Let [X_i = \left{ \begin{arrary}{l l} 1 & H\ 0 & T\ \end{arrray}\right.]

[P\left( \sum\limits_{i = 1}^{100} X_i > 64.5 \right)]

[= P\left( \sum\limits_{i = 1}^{100} X_i - 60 > 45.5\right)]

[= P\left( \frac{ \sum\limits_{i = 1}^{100} X_i - 60}{ \sqrt{24} > \frac{ 4.5}{ \sqrt{24}}]

[= 1 - \Phi(.9)]

DNHI

If [f(x) = C e^{-3x^2 + 6x}] and [f(x)] is a probability density function for the radom variable [X],

• What is [C]?
• What is [E( X)]?
• What is [Var( X)]?