$E(\operatorname{variable})$ is the expected value of a variable. $E(\operatorname{variable}|\operatorname{event})$ is the expected value of the variable conditioned on event. But what does E(variable,event) mean?
I thought it meant something like $E(\operatorname{variable}|\operatorname{event})P(\operatorname{event})$ but then I saw it written in a book where the event was certain, so the expression $E(\operatorname{variable}|\operatorname{event})P(\operatorname{event})$ would be redundant.
Thanks in advance.
Best Answer
I have seen it used in the following way: $$E(X;A) = E(1_A\, X)$$ where $1_A$ is the indicator function of a measurable set $A \subset \Omega$. (In Durrett's 'Probability: Theory and Examples')