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?
Use can use symmetry here. The problem is symmetrical in the sense that x and y can be swapped and the problem is the same. Hence, the probability that x<y must equal the probalibity that y<x. P=0.5, by symmetry.
I can start the approach. Simply integrate overt the area of interest. The geometry is simple in this case, so establishing the limits of integration is easy.