Finding k in a three-variable joint probability density function

[kasse]

Let X, Y, and Z have the joint probability density function

f(x, y, z) = kx(y^2)z, for x>0, y<1, 0<z<2

find k

$$\int_{0}^{2}\int_{- \infty}^{1}\int_{0}^{\infty}kxy^2z dx dy dz$$

This integral should equal 1. Is my procedure correct so far? I don't manage to solve the integral...

 

[HallsofIvy]

Well, that should be correct. There is going to be an obvious problem, however. That integral does not exist. If you have positive powers of variables, you cannot have infinite ranges for them. The probability distribution given, for that range of variables, is impossible.