QUIZ 2-3 - 3 8 3 5 4-= x x = 1.2 c(4 Find SD X Var X = 2 2 X E ∞ ∞-⋅ dx x f x = 2 2 3 2 2 2 1 4 3 2 3- ⋅ dx x x x = 2 2 5 4 2 1 4 3 2

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STAT 400 Spring 2011 Version C Name ANSWERS . Quiz 2 (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 be a continuous random variable with the probability density function f ( x ) = 4 3 2 3 3 2 x x - for 0 x 2, f ( x ) = 0 otherwise. a) (3) Find P ( X > 1 ). P ( X > 1 ) = 16 11 16 5 1 1 2 16 3 2 1 4 3 2 3 4 3 2 1 3 2 = = = - - - x x dx x x = 0.6875 . b) (3) Find E ( X ). E ( X ) = ( ) - dx x f x = - - = 2 0 4 3 2 0 3 2 4 3 2 3 4 3 2 3 dx x x dx x x x = 8 . 4 6 0 2 20
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Unformatted text preview: 3 8 3 5 4- -= x x = 1.2 . c) (4) Find SD ( X ). Var ( X ) = ( ) ( ) [ ] 2 2 X E- ∫ ∞ ∞-⋅ dx x f x = [ ] 2 2 3 2 2 2 . 1 4 3 2 3- -∫ ⋅ dx x x x = [ ] 2 2 5 4 2 . 1 4 3 2 3- -∫ dx x x = [ ] 2 6 5 2 . 1 2 8 1 10 3- -x x = ( 9.6 – 8 ) – 1.44 = 0.16. SD ( X ) = 16 . = 0.4 ....
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This note was uploaded on 11/28/2011 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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