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## Homework Statement

Show that E[Y^4] = 3, where Y~N(0,1)

## Homework Equations

E[(Y-mu)^4]/[E(Y-mu)^2]^2 = 3

E(Y^4) = 1/sprt(2pi)*intregral (y^4)*e^(-y^2/2)

## 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.