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Unformatted text preview: x ) = x 3 . ⇒ Y = ( ) ∑ = n i i 1 X K = ∑ = n i i 1 3 X is a sufficient statistic for τ . b) (7) Obtain the maximum likelihood estimator of τ , τ ˆ . L ( τ ) = ∏ = n i x i i e x 1 14 5 3 τ 8 τ = ∑ =∏ = n i i x n i i n n e x 1 14 5 1 3 τ 8 τ ln L ( τ ) = ∑ ∑ = = ⋅ ⋅ ⋅+n i i n i i x x n n 1 3 1 14 8 5 τ τ ln ln ln ( ln L ( τ ) ) ' = ∑ =n i i x n 1 3 5 τ = 0 ⇒ τ ˆ = ∑ = n i i n 1 3 X 5 ....
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 Fall '11
 STEPHANOV
 Normal Distribution, Probability theory, probability density function, Likelihood function, τ

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