Chapter 4: Problem 13
Let \(X_{n}\) and \(Y_{n}\) have a bivariate normal distribution with parameters \(\mu_{1}, \mu_{2}, \sigma_{1}^{2}, \sigma_{2}^{2}\) (free of \(n\) ) but \(\rho=1-1 / n\). Consider the conditional distribution of \(Y_{n}\), given \(X_{n}=x .\) Investigate the limit of this conditional distribution as \(n \rightarrow \infty\). What is the limiting distribution if \(\rho=-1+1 / n ?\) Reference to these facts is made in the Remark in Section \(2.4 .\)
Short Answer
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Key Concepts
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