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.
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.
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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.