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# 410Hw08 - STAT 410 Homework#8(due Wednesday July 22 by 4:00...

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STAT 410 Homework #8 Summer 2009 (due Wednesday, July 22, by 4:00 p.m.) Warm-up: 4.3.7 Hint: ( 29 ( 29 α β 1 1 M Gamma t t - = , t < 1 / β . 1. 4.3.2 2. 4.3.4 Hint: F Y 2 ( x ) = ( 29 ( 29 ( 29 ( 29 = - - n i i n i x x i n 2 F 1 F = ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 F 1 F F 1 1 - - - - - n n x x n x . 3. a) 4.3.9 Hint: We already know that ( 29 ( 29 1 , 0 2 Y N D n n n - . b) Find P ( 40 < X < 60 ) , where X has a ( 29 50 2 χ distribution. Hint: Use integration by parts 24 times or EXCEL: = CHIINV ( α , v ) gives ( 29 v 2 α χ for 2 χ distribution with v degrees of freedom, x s.t. P ( ( 29 v 2 χ > x ) = α . = CHIDIST ( x , v ) gives the upper tail probability for 2 χ distribution with v degrees of freedom, P ( ( 29 v 2 χ > x ) .

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4. 4.3.18 5. Let λ > 0 be an unknown parameter and let X 1 , X 2 , … , X n be independent random variables, each with the probability density function f ( x ) = ( 29 < < - - otherwise 0 1 0 1 1 λ λ x x . a) Obtain the maximum likelihood estimator of λ , n λ ˆ . b) Find the CDF of X 1 . ( not an order statistic ) c) Let W i = – ln ( 1 – X i ) , i = 1, 2, … , n . Find the CDF and the PDF of W 1 .
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410Hw08 - STAT 410 Homework#8(due Wednesday July 22 by 4:00...

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