The joint pdf (probability density function) of a random vector (X,Y) is
f(x,y) = 2( x + y - 2xy ) if 0<=x<=1, 0<=y<=1;
= 0 otherwise.
Find Pr(X > Y).
You need to integrate the pdf over the region bounded by the lines:
$\displaystyle x=y; y=0; x=1$.
This will be $\displaystyle \int_{0}^{1}\int_{0}^{x} 2(x + y - 2xy) dydx$.