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Unformatted text preview: EY = E ( E ( Y | X )), we get EY = E ( E ( Y | X )) = E ( X/ 2) = 1 / 4 . Also, we can ﬁst get the marginal density of Y by its conditional density and the marginal density of X, and then compute the expectation by deﬁnition. 4.6.7 Since Y denote the number of 6’s that show up, we have n-y rolls that are not 6’s. 3/5 those should be odd(1, 3, and 5). Thus, the distribution of X conditional on Y is binomial (3 / 5) and the conditional expectation is E ( X | Y ) = 3 5 ( n-Y ) . Similarly, the distribution of Y given X is binomial (1 / 3) and the conditional expectation is E ( Y | X ) = 1 3 ( n-X ) ....
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- Math, Probability theory, Conditional expectation, 2k, 1 k, marginal density, Pengsheng Ji