$3-$ If the probability density of $x$ is given by

$f(x)=\{\begin{array}{ccc}2x{e}^{-x^2}& \text{f}\text{o}\text{r}& x>0\\ 0& \text{e}\text{l}\text{s}\text{e}\text{w}\text{h}\text{e}\text{r}\text{e}& \end{array}$

and $Y=x^2,$ find the cumulative distribution function of $Y,$ and the p$.$d$.$f$.$ of $Y.$