st422%20hw08%20solution

st422%20hw08%20solution - Homework 8: Solutions 1 1 1 2 1...

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Unformatted text preview: Homework 8: Solutions 1 1 1 2 1 exp(-y/ ) y exp(- / ) 1 2 2 2 9.73: f ( ) y< L( ) f(y , ... | ) ln L = -nln ln L This is the MVUE of and since is a one-to-one function of , is the n i i n n i i n i i n i i y n y y n y n y y y d dx y y = = = =- = = = - = + = = = 2 MLE of which is not the MVUE of 2 2 1 1 2 1 1 1 1 1 1 2 120 130 128 2 2 3 2 9.76: a) f(y| ) exp( / ) y>0 L( ) exp( / ) ln L=-2nln ln ln L 63 b) Clearly, Y Gamma( 2, ) Thus E(Y)= 2 V(Y)= n n i i n i i n i i n n i i i i y n i i y n y n y y y y y d dx = = = = = =- + + =- =- +- = + = = = = = = = = 1 2 2 2 1 2 2 2 2 2 (2 ) 1 2 2 1 (2 ) 1 2 2 6 4 4 1 2 130 6 6 2 2 E( ) E E( ) V( ) V V( ) c) Bound for the error of estimation=2 2 V( ) 2 106.14 d) MLE of V(Y)=MLE of 2 n i i n i i y n n i n n i y n n i n n n n i p y y = = = = = = = = = = = = = = = = 2 2 2 (By Invariance property of MLEs) 2(130 ) 7938 MLE = = = 1 2 1 1 ( ) 1 1 ( ) 1 1 1 1 1 2 1 9.77 : f(y| , ) exp( / ) y>0 L( ) exp( / ) ln L=-nln ( ) n ln +ln / ln L / b) E( ) V( )...
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This note was uploaded on 03/30/2008 for the course ST 422 taught by Professor Gerig during the Spring '08 term at N.C. State.

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st422%20hw08%20solution - Homework 8: Solutions 1 1 1 2 1...

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