Hey AmbientTemple.

In your unit square you need to draw the line y = x and look at the probability of the upper triangle (Y > X) and the lower triangle (Y <= X). Once you specify the probability functions for these triangles you can get the marginals. You know that since X and Y are IID, then P(X = x, Y = y) = P(X = x)P(Y = y).

You get the marginals by integrating over the right triangles.