Transformation of Random Variable - Not Monotonic Case

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Let random variable $X \thicksim U(-2,3)$ where $U$ denotes uniform distribution. Then I'd like to derive the probability density function of $Y = X^2$

but this case not like strictly increasing or decreasing case, for example for X=3, there exists two different variable $Y$ such as $Y = \sqrt 3$ and $-\sqrt 3$

Then do I have to just allocate $1/2 \cdot 1/5$ for each case?

I've never thought of it is possible to derive pdf from not inverse mapping exisiting condition.

Any help to understand this case?