QUIZ 2-2 - P X> 0.50 = 5 1 3 3 2 3 4 3 2 1 5 2 1 5 2 = =...

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STAT 400 Spring 2011 Version B 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. Suppose the length of time (in hours) it takes for pizza to be delivered by Momma Leona’s Pizza has the probability density function < < + = otherwise 0 1 0 ) ( 2 x x x c x f a) (4) Find the value of c that makes f ( x ) a valid probability density function. Must have ( ) - dx x f = 1. Then 1 = ( ) 3 1 2 0 1 3 2 3 2 1 0 2 + = + = + c x x c dx x x c . 1 = 3 1 2 + c . 3 2 2 = c . 3 4 = c . b) (3) Find the probability that it will take more than 30 minutes for a pizza to be delivered.
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Unformatted text preview: P ( X > 0.50 ) = ( ) 5 . 1 3 3 2 3 4 3 2 1 5 . 2 1 5 . 2 + = + = + ∫ ∫ x x dx x x dx x x c = 24 19 =-= +- + 24 5 1 24 1 6 1 3 1 3 2 . c) (3) Find the average delivery time. That is, find E ( X ). E ( X ) = ( ) ∫ ∞ ∞-⋅ dx x f x = ∫ + 1 3 2 3 4 dx x x = 1 4 1 9 4 4 3 + x x = 36 25 = + 4 1 9 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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