Joint probability density function

Discussion in 'Math' started by boks, Jan 10, 2009.

1. boks Thread Starter Active Member

Oct 10, 2008
218
0
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...

Last edited: Jan 10, 2009
2. steveb Senior Member

Jul 3, 2008
2,433
469
That looks correct assuming that the joint probability function is zero everywhere else. You didn't say that explicitly, but it seems implied.

You should have no trouble evaluating that integral.