STAT 4201 Midterm: STAT 421 OSU PastExam1 2 solutions
31 Jan 2019
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Show all of your work for partial credit. This is a closed book, closed notes, closed neighbor exam. You may use a calculator and one page of notes. All necessary statistical tables are provided: (5 points) let x1, x2, xn be a random sample from a geometric distribution with parameter . First we nd the joint distribution: n f (x1, x2, xn; ) = (1 )xi 1 . )n(1 )pn i=1 xi i=1 xi, ) = ( . E(x) = (by theorem 8. 1, where denotes the population mean). The population mean for the exponential distribution is (see appendix c), and thus e(x) = , and x is an unbiased estimator of . (ii) next, we nd the variance of x. V ar(x) = 2 n , where 2 is the population variance. Plugging back into the cr lower bound in equation (1), we have. Yes, x is a consistent estimator of .
