Statistics Graduate Level Quiz
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ADVANCED TOPICS IN GRADUATE STATISTICS
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Let X=(X1,X2,X3)TX=(X_1,X_2,X_3)^{\mathsf T} have a multivariate normal distribution with mean zero and covariance matrix Σ=(210121012).\Sigma=\begin{pmatrix}2&1&0\\1&2&1\\0&1&2\end{pmatrix}. What is the conditional distribution of X2X_2 given X1+X3=2X_1+X_3=2?
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