how to calculate pdf probabilitity of i.i.d

Hello

I got this assignment to do and I have no idea where to start.

Given xi, i = 1, . . . , n, i.i.d. with pdf f(xi), Find the pdf f(x) of x = max {x1, . . . , xn}

Thanks

Answer 1

[Roger Stafford]

This is apparently homework. Here's a hint to get you started. If x is the maximum of x1,x2,...,xn, the probability that x <= c is equal to the probability that xi <= c for all i. Now, remembering that the xi are independent and have the same distribution, translate that statement into a mathematical equation and differentiate it to get the probability density. Piece of cake!