**Unformatted text preview: **θ , ω /w) and W γ (m, v), where θ , ω + , m + , and v + . Answer each of the following questions, fully justifying your answer in each case. (6) (a) Are Y and W independent? (6) (b) Is Y mean-independent of W? (6) (c) Is W mean-independent of Y? (6) (d) Are Y and W uncorrelated? (24) 3. Let Y 1 and Y 2 be random variables with the same variance, but possibly different means. Let Z 1 = Y 1 + Y 2 and Z 2 = Y 1- Y 2 . Find Cov(Z 1 , Z 2 ). (25) 4. Let X and Y be random variables. Define ε = Y - E(Y|X) and U = Y - E*(Y|X), where E(Y|X) is the population regression function and E*(Y|X) is its best linear predictor. Find Cov( ε , U)....

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- Fall '10
- DaleJ.POIRIER
- Econometrics, Regression Analysis, Variance, probability density function, Dale J. Poirier