Suppose that we have an unfair coin that its head occur with probability 0.25 Le

Question

Suppose that we have an unfair coin that its head occur with probability 0.25 Let X be the number of trials needed to get 24 heads, so that X f(x)-( .1 )(0.25)24(0.75)"-24, forx = 24, 25, Consider a random sample of 25 observations X1 ,X2PX25, each representing the number of trials to obtain 24 heads of the unfair coin. a) What is E(X)? Give your answer to three decimal places. b) What is Var(x)? c) What is E(x) ? Give your answer to three decimal places d) What is Var(x)? Give your answer to three decimal places. Neg in. 2 p 2 with mr (,)(0.25)24(075)"-24 for x Give your answer to three decimal places

Explanation / Answer

for above is a negative binomial with parameter p=0.25 and r=24

a)

E(X) =r/p=24/0.25=96

b)V(X) =r*(1-p)/p2 =288

c)

E(Xbar)=E(X) =96

d)

Var(Xbar)= V(X)/n=288/25=11.52

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