So I have two independent random variables $X$ and $Y$, $Y$ ~ $U[0, 3]$ and the density function of $X$ is as follows:
$f(x) = 1/3$ if $0\le x \le 1$
$f(x) = 2/3$ if $1\le x \le 2$
$f(x) = 0$ otherwise
I calculated the joint density of this function by multiplying them, since they are independent. And now I'm trying to find $P(Y\gt X)$
Thanks in advance!