Assignment 2 (Solution).pdf - THE UNIVERSITY OF HONG KONG...

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p. 1 THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT2601 Probability and Statistics I Assignment 2 Solution Numerical answers to other questions 1. (a) 0.3 (b) 2.15, 1.5275 (c) 0.95 2. (a) 7.9 years (b) 2.17 years. (c) 0.96 (d) $28800, $4349. 3. (a) 36 1 , 3 17 , 9 35 (b) 137 60 , 137 300 , 18769 33300 (c) 19 1 , 0, 19 72 (d) 33 1 , 33 119 , 1089 590 4.   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 5.   n n m x n x n m x p 1 , n x ,..., 2 , 1 , 0 . 6. (a)   otherwise 0 if 1 1 N y n n N n y y p (b) 1 1 n N n ,    2 1 1 2 n n n N N n 7. (a)   ! 1 1 ! 4 1 ! 3 1 ! 2 1 ! 1 k n k k p k n , n k ,..., 2 , 1 , 0 (b) 1 (c)   ! 1 k e k p , , .... 2 , 1 , 0 k 8. (a) 10.6 (b)   4 52 3 52 k k p , 49 ,..., 2 , 1 k (c) 10.6 9. (a) 36 1 2 , i Y i X P for 6 , 5 , 4 , 3 , 2 , 1 i 18 1 , j i Y i X P for 1 ,..., 2 , 1 i j ; 6 , 5 , 4 , 3 , 2 , 1 i (b) 36 , i i Y i X P for 6 , 5 , 4 , 3 , 2 , 1 i 36 1 , j Y i X P for 6 ,..., 2 , 1 i i j ; 6 , 5 , 4 , 3 , 2 , 1 i (c) 36 1 , i Y i X P for 6 , 5 , 4 , 3 , 2 , 1 i 18 1 , j Y i X P for 6 ,..., 2 , 1 i i j ; 6 , 5 , 4 , 3 , 2 , 1 i
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