So I want to calculate a distribution function from a density function. The density function is as follows: $$ f(w,z)=\frac{2w}{z}\text{ if 0<wz<1, 0<w<z} $$ To find the distribution, I tried integrating using the following expression:
Assuming[0 < y && 0 < w < 1 && 0<z, Integrate[(2 y/x) Boole[0< y < x < 1/y], {y, 0, w}, {x, 0, z}]]
A friend of mine with the same assignment told me he was getting a different result, so I tried tweaking the expression. To my surprise, an expression which I think is equivalent gives me a very different result. This is the expression in question:
Assuming[ 0<y && 0 < w < 1 && 0<z, Integrate[(2 y/x) Boole[(0 < xy < 1)&&(0<y<x)], {y, 0, w}, {x, 0, z}]]
As you can see, the only change has been to the contour conditions. What is going on here?
