# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 37: Smoothing Property of Conditional Expectation

The smoothing property of conditional expectation states that where $X, Y$ are random variables, and the random variable $\textrm{E}(Y|X)$ is the conditional expectation of $Y$ dependent on $X$, then the expectation of this random variable is simply

$\textrm{E}(\textrm{E}(Y|X)) = \textrm{E}(Y)$.