(Solved): The continuous random variable \( X \) follows the probability density function \( f_{X}(x ; \thet ...

The continuous random variable \( X \) follows the probability density function \( f_{X}(x ; \theta)=\left\{\begin{array}{ll}\frac{2 x}{\theta^{2}} \exp \left(-(x / \theta)^{2}\right) & \text { for } x \geq 0 \\ 0 & \text { for } x<0\end{array}\right. \) Find the probability density function \( f_{Y}(y) \) for the random variable \( Y \) with \[ Y=\frac{X^{2}}{\theta^{2}} \]