SOA PProbability

The joint density of $X$ and $Y$ is $f(x,y)=2$ for $0<x<y<1$ and zero otherwise. Calculate $E[X]$.

$X$ and $Y$ are independent exponential random variables with $X\sim\text{Exp}(1)$ (mean 1) and $Y\sim\text{Exp}(2)$ (mean $1/2$, rate 2). Calculate $P(X<Y)$.