I have a confusion regarding notation of the expectation. Consider the following:
$$E_x(x^2) = \sum_x x^2p(x)$$ $$E_x(x|y) = \sum_x xp(x|y)$$
So the same notation here is giving different meaning right isn't it?
Up to now I was assuming $E_x$ taking $p(x)$ and calculating the expectation. However after looking at $E_x(x|y) = \sum_x xp(x|y)$, I am a bit confused