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Unformatted text preview: ≤ k since Λ * = min ( Λ , 1 ) H : θ = θ vs. H 1 : θ ≠ θ Reject H if Λ = ( 29 ( 29 θ ˆ L θ L ≤ k Example 3 : Let X 1 , X 2 , … , X n be a random sample of size n from an Exponential distribution with mean 1 / λ . That is, f X ( x ) = x e λ λ, x > 0. H : θ = θ vs. H 1 : θ ≠ θ L ( λ ) = ∏ =n i x i e 1 λ λ = ∑ = n i i n x 1 λ λ exp . λ ˆ = X 1 . Λ = ( 29 ( 29 θ ˆ L θ L =  ∑ ∑ = = n i i n n i i n x x x x 1 1 1 1 exp exp λ λ = ( 29 { } λ λ exp x n x e n n n. Λ ≤ k ⇔ { } λ exp x x≤ c Reject H if { } λ exp x x≤ c ....
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 Spring '11
 Stepanov

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