Re: Z = U(0,1)*N(0,1) + U(0,1)*N(0,1) + ... + U(0,1)*N(0,1) is distributed how?

*Given the independence*

Var(X*Y) = E((X*Y-E(X*Y)*(X*Y-E(X*Y)) =

=E((X^2*Y^2)) - (E(X))^2*(E(Y))^2

If X~N(0,1) and Y~U(0,1)

Var(Z*U)= E(N^2)*E(U^2) = 1*1/3

Note : N^2 is a chi^2 with r=1 df, which mean value is r.
E(U^2) can be found immediately by integration

For the sum of n of these products

Var (sum (Z*U)) = n* Var(Z*U) = n/3

Sigma (sum(Z*U)) = sqrt(n/3)

I thought it was harder.

_________licas (Luis A. Afonso)
.

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