(b) \((10\%)\) Show that \(\operatorname{E}(Y|\mathbf{x}) = x + \theta\). In accordance with the theory, the expected value of \(X + \theta\) is that of Y, namely, \(3\theta / 2\), and the variance of \(X + \theta\) is less than that of Y. Show the variance of \(X\) is in face \(5\theta^2 / 4\).

阿摩線上測驗 · 2026-11-09T13:45:15+08:00

(b) (10%) Show that E(Y|x) = x + θ. In accordance with the theory, the expected value of X + θ is that of Y, namely, 3θ / 2, and the variance of X + θ is less than that of Y. Show the variance of X is in face 5θ^2 / 4.

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(b) \((10\%)\) Show that \(\operatorname{E}(Y|\mathbf{x}) = x + \theta\). In accordance with the theory, the expected value of \(X + \theta\) is that of Y, namely, \(3\theta / 2\), and the variance of \(X + \theta\) is less than that of Y. Show the variance of \(X\) is in face \(5\theta^2 / 4\).

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