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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 α . b) (7) Obtain the maximum likelihood estimator of α , α ˆ . L ( α ) = ∏ = n i x i i e x 1 11 4 3 α 2 α = ∑ =∏ = n i i x n i i n n e x 1 11 4 1 3 α 2 α ln L ( α ) = ∑ ∑ = = ⋅ ⋅ ⋅+n i i n i i x x n n 1 3 1 11 2 4 α α ln ln ln ( ln L ( α ) ) ' = ∑ =n i i x n 1 3 4 α = 0 ⇒ α ˆ = ∑ = n i i n 1 3 X 4 ....
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 Fall '11
 STEPHANOV
 Normal Distribution, Probability theory, probability density function, Likelihood function, α

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