Hi

I need to work out this integral $\displaystyle $$\int^{\infty}_{0}a^2y^2e^{\frac{-a^2y^2}{2}}dy$$$. I have already multiplied the expression by y, since i'm trying to work out E(Y).

Now I tried to look at the Gamma and Beta functions, but I can't recognise how they would work here, mainly because of the exponential part contains a $\displaystyle y^2$.

Any help is much appreciated