Suppose you have two independent random variables, and you want to find the distribution of the maximum of the two. The best way is to start with the CDF of the max. Notice that
`Pr[ max(X_1,X_2) <= z ]`
is the probability that both `X_1` and `X_2` are less than or equal to `z`. And if the two random variables are independent, then this is the probability that `X_1 <= z` times the probability that `X_2 <= z`.