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HW 2 - Questions

HW 2 - Questions - (a Suppose ± = 0 Find an estimator of...

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EC489.02 Summer 2011 Homework 2 The due date for this assignment is Thursday July 7, 13:00 . 1. Show that n X i =1 ( X i ° ° ) 2 = n X i =1 ( X i ° ° X ) 2 + n ( ° X ° ° ) 2 ; where ° = E [ X i ] for i = 1 ; :::; n and ° X = 1 n n X i =1 X i : Remember that this equality was used in proving the second part of Theorem 8 : 11 : 2. Suppose that we are given a random sample X 1 ; :::; X n of size n from a continuous Uniform population. Remember that for a random variable X i ; distributed with the continuous Uniform distribution, E [ X i ] = ± + ² 2 and V ar ( X i ) = 1 12 ( ² ° ± ) 2 where

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Unformatted text preview: (a) Suppose ± = 0 . Find an estimator of ² by the method of moments, using E [ X i ] only. (b) Suppose ± and ² are both non-zero. Show that the method of moments estimator for ² is now given by ^ ² = 1 n n X i =1 x i + v u u t 3 " 1 n n X i =1 x 2 i & 1 n 2 & X x i ± 2 # : Hint : Think about p V ar ( X ) . 1 Grading Scheme 1. 3 pts 2. 7 pts (a) 2 pts (b) 5 pts 2...
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HW 2 - Questions - (a Suppose ± = 0 Find an estimator of...

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