A is a geometric random variable and has a parameter of 1/3. B₁, B₂, B₃ and 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.