# Integration of a pdf, expected value

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Tags: expected, integration
 P: 46 1. The problem statement, all variables and given/known data Show that E[Y^4] = 3, where Y~N(0,1) 2. Relevant equations E[(Y-mu)^4]/[E(Y-mu)^2]^2 = 3 E(Y^4) = 1/sprt(2pi)*intregral (y^4)*e^(-y^2/2) 3. The attempt at a solution I have expanded and simplified the first equation above and cannot get it to equal 3. I think it's possible to solve the second using integration by parts but I can't find what to use for [u, du, dv, v] in order to integrate by parts. Any help would be appreciated. Thanks.
 P: 46 Sorry, it's a definite integral in from -inf to inf.
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Thanks
P: 5,070
 Quote by alias 1. The problem statement, all variables and given/known data Show that E[Y^4] = 3, where Y~N(0,1) 2. Relevant equations E[(Y-mu)^4]/[E(Y-mu)^2]^2 = 3 E(Y^4) = 1/sprt(2pi)*intregral (y^4)*e^(-y^2/2) 3. The attempt at a solution I have expanded and simplified the first equation above and cannot get it to equal 3. I think it's possible to solve the second using integration by parts but I can't find what to use for [u, du, dv, v] in order to integrate by parts. Any help would be appreciated. Thanks.
You might have to try several things until you get something that will work. What have you tried so far? Another approach that is often useful is to look at dI(a)/da or d^2I(a)/da^2, where I(a) = integral_{y=-inf..inf} exp(-a*y^2/2) dy.

RGV

 P: 46 Integration of a pdf, expected value I tried integration by parts but the integral I end up with makes no sense to me.