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assignment2solution

assignment2solution - 10/11 THE UNIVERSITY OF HONG KONG...

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10/11 p. 1 THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 Probability and Statistics I Assignment 2 Solution 1. Sample space: { } BO BB WO WB WW , , , , = Ω Note that the outcomes are not equally likely with associated probabilities: { } ( ) 3 1 45 15 2 10 2 6 = = = WW P , { } ( ) 5 2 45 3 6 = × = WB P { } ( ) 15 2 45 1 6 = × = WO P , { } ( ) 15 1 45 2 3 = = BB P , { } ( ) 15 1 45 1 3 = × = BO P The random variable X is the following function: ( ) 2 = WW X , ( ) 1 = WB X , ( ) 0 = WO X , ( ) 0 = BB X , ( ) 1 = BO X (a) The the possible values of X are –1, 0, 1, 2. (b) The probability mass function is given by ( ) { } ( ) 15 1 1 = = = BO P X P ( ) { } ( ) 5 1 15 1 15 2 , 0 = + = = = BB WO P X P ( ) { } ( ) 5 2 1 = = = WB P X P ( ) { } ( ) 3 1 2 = = = WW P X P The cumulative distribution function is ( ) ( ) < < < < = = 2 if 1 2 1 if 3 2 1 0 if 15 4 0 1 if 15 1 1 if 0 x x x x x x X P x F . 2. ( ) = = = = = 12 , 6 9 1 4 12 1 30 , 24 , 20 , 18 , 15 , 10 , 8 , 5 , 3 , 2 18 1 36 , 25 , 16 , 9 , 1 36 1 i i i i i p
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