# Question: Let X1 be independent random variables with

Let X1, . . . be independent random variables with the common distribution function F, and suppose they are independent of N, a geometric random variable with parameter p. Let M = max(X1, . . . ,XN).

(a) Find P{M ≤ x} by conditioning on N.

(b) Find P{M ≤ x|N = 1}.

(c) Find P{M ≤ x|N > 1}.

(d) Use (b) and (c) to rederive the probability you found in (a).

(a) Find P{M ≤ x} by conditioning on N.

(b) Find P{M ≤ x|N = 1}.

(c) Find P{M ≤ x|N > 1}.

(d) Use (b) and (c) to rederive the probability you found in (a).

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