# Maximum of one exponential and one uniformly distributed random variable

If X and Y are independent random variables with X exponentially distributed with mean 1 and Y uniformly distributed in [0,1] , how do I find the distribution of Max(X,Y)

• People here will be more willing to help if you share what have you tried and where you are stuck at. – Lord Soth Oct 27 '13 at 19:05

$\max\{X,Y\}<x$ if and only if $X<x$ and $Y<x$.