P Set 5 - 1 MGTECON 603, Econometrics I Jules H. van...

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Unformatted text preview: 1 MGTECON 603, Econometrics I Jules H. van Binsbergen and Ying Xue Fall 2009 Stanford GSB PROBLEM SET 5 Due: Monday November 2 nd 1. Let X 1 , X 2 , . . . , X N represent a random sample from each of the distributions having the following probability density functions. In each case find the maximum likelihood estimator of . (a) f ( x ; ) = x - 1 , for 0 < x < 1, and zero elswhere, for 0 < < . (b) f ( x ; ) = (1 / 2) exp(-| x- | , for- < x < , and zero elswhere, for- < < . 2. Let X 1 , X 2 , . . ., X N be a random sample from the distribution having pdf f X ( x ; 1 , 2 ) = (1 / 2 ) exp(- ( x- 1 ) / 2 ) for 1 < x < , and- < 1 < , 0 < 2 < . Find the maximum likelihood estimators of 1 and 2 . 3. Let Y 1 , Y 2 be a pair of independent, identically distributed random variables with common density f Y ( y | ) = 1 exp(- y/ ) for y > 0 and zero elsewhere, and for some > 0. Consider the estimator W...
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P Set 5 - 1 MGTECON 603, Econometrics I Jules H. van...

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