QUIZ 2-4 - 135 4 9 1 5 4- -= x x = 1.8 . c) (4) Find SD ( X...

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STAT 400 Spring 2011 Version D 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 ) = 27 3 4 9 2 4 x x - for 0 x 3, f ( x ) = 0 otherwise. a) (3) Find P ( X > 2 ). P ( X > 2 ) = - 3 2 3 2 27 4 9 4 dx x x = 27 11 27 16 1 2 3 27 1 27 4 4 3 = = - - x x 0.4074 . b) (3) Find E ( X ). E ( X ) = ( ) - dx x f x = - - = 3 0 4 3 3 0 3 2 27 4 9 4 27 4 9 4 dx x x dx x x x = 2 . 7 9 0 3
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Unformatted text preview: 135 4 9 1 5 4- -= x x = 1.8 . c) (4) Find SD ( X ). Var ( X ) = ( ) ( ) [ ] 2 2 X E- - dx x f x = [ ] 2 3 3 2 2 8 . 1 27 4 9 4- - dx x x x = [ ] 2 3 5 4 8 . 1 27 4 9 4- - dx x x = [ ] 2 6 5 8 . 1 3 81 2 45 4- -x x = ( 21.6 18 ) 3.24 = 0.36. SD ( X ) = 36 . = 0.6 ....
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