Quiz3Bans - & ~ of θ Show work E(X =& 2& 1& 1...

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STAT 410 Spring 2008 Version B Name ANSWERS . Quiz 3 (10 points) Be sure to show all your work, your partial credit might depend on it. No credit will be given without supporting work. 1. Let X 1 , X 2 , … , X n be a random sample of size n from the distribution with probability density function ( ) ( ) ( ) X X 1 ; x x f x f - = = , 0 < x < 1, θ < 1. a) (5) Find the method of moments estimator
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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.

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