Conditional Expectation

Viewed before \(Y\) is revealed, the conditional expectation of \(X\) given \(Y\) is itself a random variable — a function of \(Y\):

\[\mathbb{E}[X\lvert Y]=g(Y)\]

The mechanics of conditioning on an event or on another random variable are covered in Conditional Distributions.

Draft

This page is a partial draft — the full treatment is planned but not yet written.