Question

Exercise 2, (a:3, b:4, c:4, d:3, e:3, f:3pt.) A compulsive gambler visits a casino and sees a row of n gambling machines ("one armed bandits") He cannot stop himself from playing on each machine until he has won. The i-th machine has probability pi E (0,1) of winning. (a) Let Xi be the number of times he play machine i. Give the pmf of X4 (b) Let M min(X1,... , Xn) be the least number of times he play the same machine. Show that M has a geometric distribution and determine the parameter (c) Suppose pi = ..= pn, and write S := X1 + Xn. Given an expression for P(S k) (d) When is an N-valued random variable memory free? (e) Show that every geometric random variable is memory free. (f) Let Y be an N-valued random variable that is memory free. Show that Y must have a geometric distribution

Answer 1

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