# Random variable X and Y have the joint PDFf_{XY}(x,y)=\begin{cases}c,\ x

Random variable X and Y have the joint PDF

Find the marginal PDF ${f}_{Y}\left(y\right)$.

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Luvottoq

The marginal PDF ${f}_{Y}\left(y\right)$ is obtained as given below:

$f\left(y\right)={\int }_{x}f\left(x,y\right)dx$
$={\int }_{0}^{\sqrt{1-y}}\frac{3}{2}dx$
$={\left[\frac{3}{2}x\right]}_{0}^{\sqrt{1-y}}$
$=\frac{3\sqrt{1-y}}{2}$
$f\left(y\right)=\frac{3\sqrt{1-y}}{2};0\le y\le 1$