# Probability density function. Find $k$

Let $f_{X,Y}(x,y) = kxy$, for $0 ≤ x, y ≤ 1,$ otherwise $f_{X,Y}(x,y) = 0$.

(a) Determine $k$ such that $f_{X,Y}(x,y)$ is a PDF.

-
Reminder: A property of PDF is such that its integral over its domain equals what. Apply your calculus. I think you know what the what is. – Frenzy Li Aug 12 '12 at 12:26

As implied, $\int_{R^2} f_{X,Y}(x,y)=1$. (Property of PDF)
Thus $\int_0^1\int_0^1 kxy dxdy=1$, with the rest being mere integration.
@Panda Yep, that's the answer. Harder questions involve triangular or circular area of integration which will just complicate integration, though-- e.g. $0<=x<=y<=1$. – Frenzy Li Aug 12 '12 at 12:43