# Normalizing a Joint PDF

Probability Level 2

A certain joint PDF for two random variables $X$ and $Y$ is given by the following expression:

$f_{XY} (x,y) = Cxy e^{-y^2},$

where $Y$ is drawn from $(0,\infty)$ and $X$ is drawn from $[0,1]$.

Find the normalization constant $C.$

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