Variance of X squared


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If you know the distribution then you can calculate.
var(Z) =E[ (Z^2-E[Z])^2 ]
var(Z^2) =E[ (Z^4-E[Z^2])^2 ]
vinux I think you mixed up a little bit. I know of two equivalent ways of getting variances but it looks like you combined them to get something wrong.

\(Var(Z^2) = E[(Z^2 - E[Z^2])^2] = E[Z^4] - E[Z^2]^2 \)
on internet I found something like:
but there is the assumption of Yand X independent, that is hardly my case.

Probably I am complicating too much the question, so I give you the equation I have to solve, because probably there is an easier solution:

E[-e^-alpha(Y+Z)^2] that is:
-e^-alpha[E[Y+Z]^2-alpha/2*var[(Y+Z)^2] with Y and Z distributed as normal

thank you
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