probability density function for a random variable For a given probability density function $f(x)$, how do I find out the probability density function for say, 
$Y = x^2$?
$$f(x)=\begin{cases}cx&,0<x<2\\2c&,2<x<5\\0&,\text{otherwise}\end{cases}$$

HINT 1: Note that $P(Y < 0) = 0$ (since $Y = X^2 \geq 0$) and for $y >0$,
\begin{gather*}
P(Y \leq y) = P(X^2 \leq y) = P(-\sqrt{y} \leq X \leq \sqrt{y}) = \dots
\end{gather*}
HINT 2: For any $z \in \mathbb{R}$, $P(X \leq z) = \int_0^z f(x) dx$. Now evaluate the integral as a piecewise function, from $0$ to $2$ and then from $2$ to $5$, and plug back into HINT 1. 
