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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

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up vote 0 down vote accepted

Use change of variables. Let $y=x^2$ and then it becomes a gamma distribution.

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thank you i got it! – user43126 Sep 30 '12 at 23:20

You probably know how to integrate $\int_0^\infty e^{-x^2} dx$. This is indeed quite the same after two times partial integration.

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thank you! i got it – user43126 Sep 30 '12 at 23:21

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