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Question 1: Recall, from your lecture slides, that if X1 is a chi-square random variable with v1 degrees of freedom, and X2 is a chi-square random variable with v2 degrees of freedom, and X1 and X2 are independent, then Z = X1 + X2 follows a chi-square distribution with (v1 + v2) degrees of freedom. Suppose that X3 is a chi-square random variable with v3 degrees of freedom, and it is independent of both X1 and X2. Then the random variable, Y = (X1 + X2 - X3) does not follow a chi-square distribution!
(a) What is the mean of the random variable, Y? What is the variance of Y?
(b) Suppose that we have n1 random sample values from the distribution of X1, n2 random sample observations from the distribution of X2, and n3 random sample observations from the distribution of X3. Suggest an unbiased estimator for the mean of Y that you have stated in part (a)
(c) Suggest an unbiased estimator for the variance of Y that you have stated in part (a).
(d) Are the estimators that you have suggested in parts (b) and (c) consistent? Why or why not?
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A clinic finds that it can reduce costs by eliminating appointments. The clinic is able to eliminate some telephone staff, and physicians become more productive. Patients wait until the physician is available, so the physician has virtually no downti..
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You are a manager in a perfectly competitive market. The price in your market is $35. Your total cost curve is C(Q) = 10 +2Q +.5(Q^2). What level of output should you produce in the short run? What price should you charge in the short run? Will you m..
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The data-plotting tool will automatically connect the points with a line.
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