Conditional expected value

Projection interpretation of conditional expected value

Let be real random variables. For any function , #m/thm/prob

implying , i.e. is completely uncorrelated with any function of . This motivates the following interpretation of conditional expectation:

Projection interpretation of conditional expected value

contains the entire component of which is a function of (i.e. determined by ) and the residual component is completely uncorrelated with any function of .

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