Then how do i find the mean of $\int_0^\infty\frac4{\sqrt{\pi} b^3}x^2e^{-x^2/b^2}dx;$ if so do how do i do this using the gamma distribution? is there a short cut or do i have to do integration by parts?please explain.
I proved it is a PDF using polar coordinates but wonder if there is not a quicker way using the gamma distribtution. my book and the internet have not been helpful