# Math Help - conditional expectation

1. ## conditional expectation

what is X*E(X|G)? Is it just E(X^2|G)?

and What is E[(E(X|G))^2] ?

2. Originally Posted by Kat-M
what is X*E(X|G)? Is it just E(X^2|G)?
No. Take $M_t$ to be a martingale, then $M_t\mathbb{E}[M_t|\mathcal{F}_s]=M_tM_s \neq \mathbb{E}[M_t^2|\mathcal{F}_s]$
and What is E[(E(X|G))^2] ?
It is exactly what you wrote.