Let $X$ and $Y$ be two independent random variables having the same uniform distribution $U(0,1)$ with density
$f(x)=1$ if $0≤x≤1$ (and $0$ elsewhere).
Let $Z$ be a real random variable defined by:
$Z=X-Y$ if $X>Y$ (and $0$ elsewhere).
Derive the distribution of $Z$.
Compute the expectation $E(Z)$ and variance $V(Z)$.