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Unformatted text preview: 2 (1). (b) Let X 1 ,X 2 ,... ,X n iid N (0 , 1). ind the distribution of Y = n i =1 X 2 i . 5. Let X 1 ,X 2 ,... ,X n be a random sample of size n from a population whose density (pdf) is given by f ( x ) = x -1 / I (0 , ) ( x ) where > 0 is a known Fxed value, but is unknown. Consider the estimator = max( X 1 ,X 2 ,... ,X n ). (a) Show that is a biased estimator of . (b) ind a multiple of that is an unbiased estimator of . (c) ind the variance of your estimator from part (b). 6. Required for 5520 Students Only Let X 1 ,X 2 ,... ,X 10 be iid random variables from a distribution with moment generating function M ( t ) = 1 3 b 1-2 3 e t B-1 , for t <-ln(2 / 3) . ind P p 10 s i =1 X i > P ....
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- Fall '11