Probability density function. Find $k$

Question

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.

Answer 1

Selected from PDF at WikiPedia.

The probability density function is nonnegative everywhere, and its integral over the entire space is equal to one.

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.