410Hw08 - STAT 410 Homework #8 Summer 2009 (due Wednesday,...

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Unformatted text preview: STAT 410 Homework #8 Summer 2009 (due Wednesday, July 22, by 4:00 p.m.) Warm-up: 4.3.7 Hint: ( 29 ( 29 1 1 M Gamma t t- = , t < 1 / . 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 , 2 Y N D n n n - . b) Find P ( 40 < X < 60 ), where X has a ( 29 50 2 distribution. Hint: Use integration by parts 24 times or EXCEL: = CHIINV ( , v ) gives ( 29 v 2 for 2 distribution with v degrees of freedom, x s.t. P ( ( 29 v 2 > x ) = . = CHIDIST ( x , v ) gives the upper tail probability for 2 distribution with v degrees of freedom, P ( ( 29 v 2 > x ) . 4. 4.3.18 5. Let > 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 1 1...
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This note was uploaded on 10/29/2009 for the course STAT 420 taught by Professor Stepanov during the Spring '08 term at University of Illinois at Urbana–Champaign.

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410Hw08 - STAT 410 Homework #8 Summer 2009 (due Wednesday,...

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