Chapter 4 The Multivariate Normal Distribution
Then the conditional distribution of , given that , is normal and has . and . [proof:] We only need to prove , then, . By taking . so . By the result (page 2 or Result 4.3 in textbook), , where. Since and have zero covariance, they are independent. Therefore, the conditional distribution is the same as the unconditional distribution of . ................
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