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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 e- x if x > otherwise (This is an exp ( 1 ) distribution with expectation equal to E ( X ) = and variance V ( X ) = 2 .) Consider the following estimators for ....
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- Fall '07