Calculating Joint Probability for f(x,y) = 4xy with X<Y in 0<x<1 and 0<y<1

[kasse]

If

f(x,y) = 4xy, for 0<x<1, 0<y<1
f(x,y) = 0, elsewhere

What's the probability that X<Y?

It seems likely that the probability is 0.5, but how can I show it matematically?

 

[Unco]

Hi Kasse,

If f is the joint probability density function, then P(X<Y) is the double integral of f(x,y) over the region in the unit square given by y>x.