Solved – Finding a pdf of an exponential distribution

Random variable $X$ is distributed exponentially with mean 1.
Find the pdf of $Y=(X-1)^2$

I'm not quite sure what this question is asking. Could anyone help me out?

I assume this is homework, so I'll just outline the answer.

This is about transformations of pdfs. You know the distribution of the variable $X$, which is exponential. Exponential distributions have only one parameter, which you'll have to determine backwards from the mean value.

Then you transform the distribution $X longrightarrow Y(X)$. If you do the calculation, then you'll yield a pdf for Y.

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