Question: 11. Show that conditional expectation is an orthogonal projection in the sense that it satisfies the Pythagorean identity 8 (Y' ) = 8{[8(Y] ) ]'

11. Show that conditional expectation is an orthogonal projection in the sense that it satisfies the Pythagorean identity 8 (Y' ) = 8{[8(Y] ) ]' } + 8{[Y - 8(Y19) 1} and the random variables 8(Y|9) and [Y -8(Y|$ )] are orthogonal, 8 8(YO) [Y - 8(Y)]) = 0

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