st422%20hw06%20solution

st422%20hw06%20solution - Solutions Homework 6 1 1 1 2 1 1...

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Unformatted text preview: Solutions: Homework 6 1 1 1 2 1 1 1 2 1 2 1 1 1 1 9.29 : , ... are iid Bernoulli(p) variates P(X=x|p)=p (1 ) L(X ,X ...X |p)= P(X =x|p) p (1 ) p (1 ) 1 ( , ) ( , ,... ) By thm 9.4, is suffi n n i i i i i i n x x n n n X n X x x n i i n i i i n i i Q X X X p p p g X p h x x x X = =--- = = = =- ∑ ∑ =- =- × = ∑ ∏ ∏ ∑ cient for p ( ) ( ) ( ) 2 2 2 2 2 2 2 2 1 2 2 ( ) 1 2 2 1 ( ) 1 2 2 1 ( 2 1 2 2 1 1 2 Q 9.30: , ... is a r.s from N( , ) distribution a) is unknown and is known L( ) exp ( ) exp( ( ) exp( ( ) exp i i i i n n y i n y n i n y y n i n Y Y Y μ σ π σ μ σ π σ μ μ σ π σ σ π μ σ μ σ μ- =- =- + = =- =- =- = ∏ ∑ ∑ { } ( ) 2 2 1 2 2 2 2 (2 ) 2 2 1 2 2 ( ) 1 2 2 1 ( 1 2 exp ( , ) ( , ... ) by factorization thm Thus, is sufficient for ) is known and is unknown L( ) exp ( ) exp( n i i i i y nY n n n y i y n g y h y y y Y b μ σ σ μ σ π σ σ π μ μ μ σ μ = +- =- ∑...
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st422%20hw06%20solution - Solutions Homework 6 1 1 1 2 1 1...

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