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).

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