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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10/11 p. 2 3. () + + = n n m i n i n m i p 1 , n i ,..., 2 , 1 , 0 = 4. (a) 55 1 = c , 7 = μ , (b) 6 2 = σ 25 12 = c , 25 48 = , 625 696 2 = (c) 9 1 = c , 0 = , 9 8 2 = (d) 9 1 = c , 9 23 = , 81 38 2 = 5. 0, 9 8 , 9 52 6. Not fair, 9 5489 7. (a) 15 1 (b) 45 49 8. (a) 29 (b) 61.72 (c) Both are telling the truth. 9.
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This note was uploaded on 01/16/2012 for the course STAT 1301 taught by Professor Smslee during the Fall '08 term at HKU.

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

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