Hi, I got stuck with the question 3.20 b) in casella and berger 2nd (no solution for this question in the pdf solution manual)
The question ask u to find the transformation Y=g(X) and the values of alpha and beta that transforms the folded normal into gamma(alpha,beta)
If x~folded normal(0,1), then y = sum{i=1 to k} x^2 ~ chi-square(k), where k = d.o.f.
Because the chi-square(k) is a special case of the gamma(a,b) where a = k/2 and b = 1/2.
Thus, given x~folded normal(0,1), g(x) = sum{i=1 to 2a} x^2 ~ gamma(a,1/2).
Hope it helps!!
Traxex, Iesiadot