True/False?
Let X,Y by random variables. If X^{2} has an expectation (not necessarily finite), then (E(X|Y))^{2} has an expectation.
In other words, if E(X^{2} ) exists, does E(E(X|Y) E(X|Y)) exist?
True/False?
Let X,Y by random variables. If X^{2} has an expectation (not necessarily finite), then (E(X|Y))^{2} has an expectation.
In other words, if E(X^{2} ) exists, does E(E(X|Y) E(X|Y)) exist?
I meant a finite expectation (of the absolute value for $\displaystyle $X$$). If the expectation of $\displaystyle X^2$ is finite the result holds using Jensen's inequality. So we have to deal with the case $\displaystyle E[X^2]=+\infty$.