Assignment 3 (Solution).pdf

Assignment 3 (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 3 Solution Numerical answers to other questions 1. (a) 4 3 (b)   1 1 1 1 3 2 4 1 1 0 3 x x x x x x F X (c) 0, 5 1 (d) 0.6575 2. (a)   5 0 5 5 1 x x x x F (b) 12 5 (c) both are infinite (d) 4.472 6. (a) 30, 150 (b) 8, 8 (c) 3, 8 (d) 8.4, 2.52 (e) 12, 36 7. (b)   1 exp t X e t M for all t 8. (a)   . 0 if 2 1 1 , 0 if 2 1 y e y e y F ay ay Y (b)   2 2 2 t a a t M Y , a t a (c) 0, 2 2 a 9. (a) 0.5 (b) 0.5 11.   2 3 2 1 1 1 30 t t T e t e t t t f , 0 t 12. 0.4724, 0.5455 13. (a) 0.1353 (b) 0.1353 14. (a) 2 A (b) 2 log 15. 402.12, 808517.99 16. (a) 0.0375 (b) 0375 . 0 , 4 Gamma (c) 106.67, 2844.44 (d) 0.05 18. 0.05 19. (a)   r t t X p e p e t M 1 1 , p t
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