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Unformatted text preview: 2028A: Basic Statistical Methods Homework 3 This homework is due Thursday, September 22nd in class BEFORE class starts . Late papers will not be accepted. Please do not turn in any papers to any mailbox. • Please remember to staple if you turn in more than one page. • You must SHOW ALL WORK. If you do not show your work, you may not receive full credit. I Point Estimation 1 7.41 (a) and (b) 2 Assume X 1 ,...,X n is a sample of independent and identically distributed random variables from the uniform U (0 ,a ). We make inference on the parameter a . (a) Find a method of moments estimator for a . (b) Find the maximum likelihood estimator for a . Denote the MLE with a of a . (c) Given that the expectation of E ( a ) = na n +1 , show that the bias of a converges to zero as n →∞ . (d)Propose an unbiased estimator for a . 3 7.13 page 231 III Comparing Estimators 1 Let X 1 ,X 2 ,X 3 be a random sample from the following distribution: f X ( x ) = 1 θ e- x θ if x > otherwise (This is an exp ( 1 θ ) distribution with expectation equal to E ( X ) = θ and variance V ( X ) = θ 2 .) Consider the following estimators for θ ....
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- Fall '07
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