Hey gordo151091.

You have f(Y|X)(y|x) = 1/(2x - 0.5x) since distribution of a uniform is 1/(b-a) given U(a,b). However this doesn't work when x = 0. Anyway, using fy(y) = integral over X f(x,y)(x,y) = Integral over x f(y|x)*fx(x) = 1/(2x - 0.5x) * (-x^2/75 - 6x/75 + 8/15).

We should check our pdf as well. Integral over x f(x)dx = [-x^3/225 - 3x^2/75 + 8/15x]{3,0} = -27/225 - 27/75 + 24/15 = 1.12 != 1. This means given my assumptions, you have an invalid PDF function.