Hi all, I guess a little confusion with covariances here. the solution suggests that E(Z+Z_)=E(Z+*Z-), even though the two are not independent. I didnt know this was allowed. Can we always compute the joint expectation this way? Thanks Molly
Hi Molly In this question the random variables are not independent but are uncorrelated, cov(Z-Z+)=0. E(Z-Z+)=E[(X-Y)(X+Y)]=E(X^2-XY+XY-Y^2)=E(X^2-Y^2)=E(X^2)-E(Y^2)=0 for these random variables of Z+ and Z-. This is part of the simplified covariance formula cov(Z+Z-)=E(Z-Z+)-E(Z-)*E(Z+). Thanks Andrea
