A certain random variable X has a a normal distribution with \[Mu] = 0 and \[Sigma] = 1. Come up with a formulas for the cumulative distribution function and probability density function of X^2 and plot each separately.
Would this be right ? Prob[X^2 <= x] = Prob[-Sqrt[x] <= X <= Sqrt[x]] = Xcdf[Sqrt[x]]- Xcdf[-Sqrt[x]].
If , you've already derived . Just take the derivative with respect to y to get the pdf of Y in terms of the pdf of X, which you have a closed form expression for. You should recognize the form of the pdf straight away and know that there isn't a closed form formula for the cdf.