Probability density of Z = XY for random point in unit square

[RussianWinter]

Homework Statement

position of a random point with coordinates (x; y): equal probability inside a square whose side is 1 and the center of which coincides with the origin. Determine the probability density of Z = XY

Homework Equations

The Attempt at a Solution

 

[LCKurtz]

Since the joint density of Z = XY is uniform on the square the probabilities agree with areas. Have you worked out the area corresponding to xy <= z in the square for various z?