Read this thread: http://www.mathhelpforum.com/math-he...tml#post119542
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]].
Read this thread: http://www.mathhelpforum.com/math-he...tml#post119542
He can do what he is doing and just take the derivative of the expression he already has to get the pdf. Transformation method is fine too, but some intro texts don't cover transformations that are only monotone on intervals (mine didn't, at least).
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.