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Stat 5131 (Geyer) Second Midterm Solutions

Stat 5131 (Geyer) Second Midterm Solutions - Problem 4 The...

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Up: Stat 5131 Stat 5131 Midterm 2 Problem 1 By a special case of the parallel axis formula Hence and Problem 2 (a) The expectation of a sum is the sum of the expectations, hence . (b) The general formula for a variance of a sum is In this case, all of the covariance terms are zero except when j = i + 1, so Since and ,
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Problem 3 (a) We can find E ( X ) and E ( X 2 ) in one shot, by evaluating Then the case k = 1 gives E ( X ) = 4 / 3. (c) By the case k = 2 in the formula above, E ( X 2 ) = 4 / 2 = 2. Then use
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Unformatted text preview: Problem 4 The joint density is To find the marginal of Y we integrate out X , being careful about the range of integration. When we fix Y = y , the range of X is . Problem 5 Everyone should know that the regression function asked for in the problem is . The easy way to find it is to use the formula without first calculating the conditional p. d. f. In this problem g ( x ) = x . So the numerator is Up: Stat 5131 Charles Geyer 11/14/1998...
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