Re: Jointly Gaussian Random Variables

On Feb 29, 6:24 pm, "Manolis C. Tsakiris" <el01...@xxxxxxxxxxxx>
wrote:
Hello,

let x and y be zero-mean, jointly Gaussian random variables and let E[] be
the expectation value operator. Then is it true that

E[(x^3)y] = E[xy] * E[x^2] ?

Hint: E[X^3Y] = E[E[X^3|Y]}. Conditioned on the value of Y, X is a
Gaussian random variable (with nonzero mean m that depends on the
value of Y). The value of E[X^3|Y] is m^3 + 3ms^2 where s^2 is the
conditional variance of X given the value of Y. The result is a
function
of Y Then, compute the expectation of this function of Y and see if
your identity holds or not.

Hope this helps

Dilip Sarwate
.

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