Unformatted text preview: the sample mean. Find the expectation and standard error of the sample mean. 5. Let X and Y be random variables such that V ar ( X ) = σ 2 , V ar ( Y ) = τ 2 , and Cov ( X, Y ) = γ . Let a, b, c, d be constants. Find Cov ( aX + bY, cX + dY ) in terms of the seven constants in this problem. 6. 7.24. This problem gives you another reason to use the sample mean as your estimate. Careful when you compute the variance  the sample is being drawn without replacement. 7. 7.37. Note that the problem doesn’t say that the surveys were based on sampling without replacement from the population. So despite the notation, don’t assume that either of the two estimates is our old friend the sample mean. 8, 9, 10. 7.28, 7.29, 7.30. In the last one, I look forward to ﬁnding out what you consider to be “plausible”. 1...
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 Spring '12
 jagoda
 Standard Deviation, Standard Error, Variance, A. Adhikari

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