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).

Find by conditioning on N

At the first glance I didn't quite understand the information given in this problem. But after a while I wrote down what I believe is asked to solve in the problem

But this is as far as I can go, I know P(k) = p(1-p)^(k-1), and I'm clueless on what's

I want to say that is independ of , but I'm not sure whether it's true.

Helps would be appreciated, thanks!