Suppose that $X$ has a uniform distribution on the interval $(−1, 1)$ with probability density function $$f(x)=\left\{\begin{array}{rl} 1/2 & \text{for }− 1 < x < 1 \\ 0 & \text{otherwise} \end{array}\right.$$
Q1: Use the cumulative distribution function (cdf) method to first find the cdf of $Y = x^2$ and hence determine the probability density function of $Y$.
Q2: Sketch the pdf of $Y$
Ans: I think I know how to do this for the interval $(0,1)$ but amn't sure what changes when the interval is different
Hint: First consider $P(Y \leq y)$ as usual. Now if you have $a^2<0.5$ what can you say about possible values of $a$? Try applying similar approach.