Let X1, . . . be independent random variables with the common distribution function F, and suppose

Question:

Let X1, . . . be independent random variables with the common 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). Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...