Normalizing a Joint PDF

Discrete Mathematics Level pending

A certain joint PDF for two random variables \(X\) and \(Y\) is given by the 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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