Conditional expectation definition

Conditional expectation definition

[jorsch]

Better than what my professor gave. Here's how he defined it:

"Let X and Y be two random variables. We denote by E(X|Y = y)
the expected value of the conditional distribution of X given Y = y. The
conditional expectation of X given Y is denoted by E(X|Y ) and is defined
to be E(X|Y = y) on the event Y = y."

Kind of circular if you ask me.