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Unformatted text preview: . Note that the distribution of X has pdf f X ( x  ) = ex , 0 x . a) Write the sample distribution f v X ( vx  ). b) Find a sucient statistic for . c) What is the MLE of ? d) What is the mean squared error of the MLE? Section III. 1. [25 points] Suppose the random variables Y 1 , . . ., Y n satisfy: Y i = + x i + i , i = 1 , . . ., n, where x 1 , . . ., x n are xed constants, and 1 , . . ., n are iid normal(0 , 2 ), 2 unknown. a) Find a threedimensional sucient statistic for ( , , 2 ). 4 b) Express the MLE of as a linear function of the statistics from part a) and . c) Express the MLE of as a linear function of the statistics from part a) and . d) Suppose 2 and are Fxed. What is the MLE of ? Is this estimator biased or unbiased? e) Suppose 2 and are Fxed. What is the MLE of ? Is this estimator biased or unbiased? 5...
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This note was uploaded on 11/29/2011 for the course MATH 4056 taught by Professor Staff during the Fall '08 term at LSU.
 Fall '08
 Staff
 Statistics, Bernoulli

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