Find the conditional expectation of ( a ) Y given X and (b) X g... | Filo
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Find the conditional expectation of ( a ) Y given X and (b) X g... | Filo
Solution For Find the conditional expectation of ( a ) Y given X and (b) X given Y in Problem 2.29, page 62 .
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SOLVED:Show that conditional expectation is an orthogonal projection in the sense that it satisfies the Pythagorean identity ℰ(Y^2)=ℰ{[ℰ(Y |ℱ)]^2}+ℰ{[Y-ℰ(Y |ℱ)]^2} and the random variables ℰ(Y |ℱ) and [Y-ℰ(Y |ℱ)] are orthogonal, ℰ{ℰ(Y |ℱ)[Y-ℰ(Y |ℱ)]}=0 .
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