h=x+jy , where x and y are Gaussian random variable with zero mean and variance is one
square root of (x^2+y^2)==> expand it using binomial theorem then take expectation value of every term, use the following equations
E(XY)=E(X)E(Y)
E(X^2)=Var(X)+[E(X)] ^2
i hope, it will be helpful
If they are Gaussian and independent, then the sum of the square will be chi-square distribution. You can follow solution on:
https://math.stackexchange.com/questions/1059938/whats-the-expectation-of-square-root-of-chi-square-variable
Yes, when each varibale is N(0,1) then X^2 is chi(1), then X^2+y^2 is aslo chi(2)
or
E(X^2+Y^2)=E(X^2)+E(y^2)
and E(x^2)=var(x)+[E(X)]^2 this =1+0=1 and the same result of E(y^2)
then
E(X^2+Y^2)=E(X^2)+E(y^2)=1+1=2 as above result of chi.
Best regards
How to find the expectation of square root of (X^2+X^2) where X and Y can be independent continuous or discrete random variables, not just standard normals?
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