st422%20hw07%20solution

# st422%20hw07%20solution - HW 7 Solutions 2 1 2 2 2 1 1 1...

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Unformatted text preview: HW 7: Solutions: 2 1 2 2 2 1 1 1 9.51: Poisson( ) E(Y)=V(Y)= E(C)=E(3Y ) 3E(Y ) 3[V(Y) {E(Y) }] 3( ) exp( ) L(y| )= exp( ) / ! { exp( )} {1/ !} ! is sufficient for by Factorization thm Now, n i i i y n n n y nY i i i i i i Y n y n y y Y 2 2 2 2 2 2 E( ) ( ) V( ) [ ( )] ( / ) ˆ ˆ ( / ) MVUE for E(C)= 3[ {1 (1/ )}] Y E Y Y E Y n Y Y Y n Y Y n 2 2 2 2 2 2 2 2 2 2 2 4 2 2 9.56: ) We know that is MVUE for . If we use as the MVUE, E( ) ( ) [ ( )] (1/ ) E( (1/ )) ˆ (1/ ) ) ˆ ( ) ( (1/ )) ( ) ( ) [ ( )] We use a lemma called Stein's lemma which sa a Y Y Y V Y E Y n Y n Y n b V V Y n V Y E Y E Y 2 2 4 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ys If X ( , ) and g is a differentiable function of X E(g(X)(X- )) [ ( )] ( ) ( ( )) ( ( )) ( ) 3 ( ) [ ( )] 3 ( ) 2 ( ) ( ) (3 ) ( ) 2 (3 )( ) 2 N E g X E Y E Y Y E Y Y E Y E Y E Y Y E Y E Y E Y E Y...
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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%20hw07%20solution - HW 7 Solutions 2 1 2 2 2 1 1 1...

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