Unformatted text preview: & ~ of θ . Show work. E(X) = ( ) ( ) & 2 & 1 & 1 1 & X== & & ∞ ∞ ∞⋅ ⋅ dx x x dx x f x . & 2 & 1 1 1= = ± = ⋅ x x n n i i . x x= 1 2 1 & ~ . b) (5) Find the maximum likelihood estimator & ˆ of θ . Show work. L( θ ) = ( ) ∏ =n i i x 1 & & 1 . ln L( θ ) = ( ) ± = ⋅n i i x n 1 ln & & 1 ln . ( ) ± == n i i d d x n 1 ln & 1 & & L ln = 0. ± = + = n i i x n 1 ln 1 & ˆ ....
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This test prep was uploaded on 04/13/2008 for the course STAT 410 taught by Professor Alexeistepanov during the Spring '08 term at University of Illinois at Urbana–Champaign.
 Spring '08
 AlexeiStepanov
 Probability

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