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Chapter 4: Q.4.36 (page 166)

Consider Problem 4.22 with i = 2. Find the variance of the number of games played, and show that this number is maximized when p = 1 2 .

Short Answer

Expert verified

In the given information the variance is maximized when p=1/2

Step by step solution

01

Step 1:Given Information

The random variable Xdenotes the number of games played.

Observe that X鈭�2,3

X can be written as X=2+IIistheindicatorrandomvariable

P(I=1)=2p(1-p)

02

Step 2:Explanation

Variance of the derivative is :

Var(X)=Var(2+I)=Var(I)=2p(1-p)路p2+(1-p)2

03

Step 3:Final Answer

Root of the derivative is 鈬�-2(2p-1)3=0鈬�p=12

鈬�-2(2p-1)3=0鈬�p=12

The variance is maximized whenP=12

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