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Unformatted text preview: ⋅ . ⇒ K ( x ) = x . ⇒ Y = ( ) ∑ = n i i 1 X K = ∑ = n i i 1 X is a sufficient statistic for β . b) (7) Obtain the maximum likelihood estimator of β , β ˆ . L ( β ) = ∏ = n i x i i e x 1 4 β 12 β = ∑ =∏ = n i i x n i i n n e x 1 4 1 β 12 β ln L ( β ) = ∑ ∑ = = ⋅ ⋅ ⋅+n i i n i i x x n n 1 1 12 4 β ln ln β ln ( ln L ( β ) ) ' = ∑ =n i i x n 1 4 β = 0 ⇒ β ˆ = ∑ = n i i n 1 X 4 ....
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 Fall '11
 STEPHANOV

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