Quiz3Bans - & ~ of . Show work. E(X) = ( ) ( )...

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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: &amp; ~ of . Show work. E(X) = ( ) ( ) &amp; 2 &amp; 1 &amp; 1 1 &amp; X--=-= &amp; &amp; - dx x x dx x f x . &amp; 2 &amp; 1 1 1--= = = x x n n i i . x x--= 1 2 1 &amp; ~ . b) (5) Find the maximum likelihood estimator &amp; of . Show work. L( ) = ( ) =-n i i x 1 &amp; &amp; 1 . ln L( ) = ( ) = --n i i x n 1 ln &amp; &amp; 1 ln . ( ) =---= n i i d d x n 1 ln &amp; 1 &amp; &amp; L ln = 0. = + = n i i x n 1 ln 1 &amp; ....
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