I've got 2 independent draws from these two distributions :$X\sim U(0,1)$ and $Y\sim U(0,2)$.
I want to find $E(\max(X_,Y))$.
I know that for two (0,1) independent Uniforms:
However now when the support changes I'm struggling to figure it out. I thought maybe splitting it over the 2 supports because when z leaves X's support the CDf is 1. I tried to do a conditional thing like: $P(\max(X,Y)<z |z<1)$ but then I'd have to find P(z<1).
Context: Mechanism design problem with 2 bidders in a first price sealed bid auction so I wanted to calculate expected revenue.