A is a geometric random variable and has a parameter of 1 3 B 1 , B 2 , B 3 and so on are uniform random variables with parameters (0,1) All of them are independent i) If C max(B 1 B A ), what is the value of t such that P(C t) Also calculate E(C) and Var(C), to 7 decimal places ii) If D min(B 1 B A ), what is the value of t such that P(D t) Also calculate E(D) and Var(D), to 7 decimal places

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Question: A is a geometric random variable and has a parameter of 1/3. B 1 , B 2 , B 3 and so on are uniform

A is a geometric random variable and has a parameter of 1/3. B₁, B₂, B₃and so onare uniform random variables with parameters (0,1). All of them are independent.

i) If C = max(B₁...B_A), what is the value of t such that P(Ct)? Also calculate E(C) and Var(C), to 7 decimal places.

ii) If D = min(B₁...B_A), what is the value of t such that P(Dt)? Also calculate E(D) and Var(D), to 7 decimal places.

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