Hello,

Their joint pdf, that is to say the pdf of (X,Y) is the product of their pdf, since they're independent.

It equals 1, for 0<x<1 and 0<y<1.

Then, use the Jacobian transformation that transforms (X,Y) into (XY,Y) (see here : http://www.mathhelpforum.com/math-he...ion-r-v-s.html for more information) to get the joint pdf of (XY,Y)

Then integrate with respect to the second variable to get the pdf of XY