$X_1$ and $X_2$ are independent with $\Gamma(p, 1)$ and $\Gamma(p + 1, 1/2)$.
Show that $Y = 2\sqrt{X_1 X_2}$ has a $\Gamma(2p, 1)$ dist.
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1Welcome to MSE, Mr. Nobel. Please read our FaQ and help section. We would like to know what you have tried and where you are stuck. Also, thank you for Dynamite. – Nick Sep 29 '14 at 16:06
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1i tried to solve the problem using mgf , and also the cdf. but tboth the cases i got some weird form. i also tried to use change of variable technique. that one works for X1+X2, but becomes complicated for the product.one more thing, this is not a homework problem or neither to gain any score from any exam or anything else. i am just curious to know. – Benzamin Sep 29 '14 at 20:57