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STAT1301 (Assig2 ans)

STAT1301 (Assig2 ans) - 09/10 THE UNIVERSITY OF HONG KONG...

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09/10 p. 1 THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 Probability and Statistics I Assignment 2 Solution 1. (a) (b) 2 , 1 , 0 , 1 ( ) = = = = = 2 3 1 1 5 2 0 5 1 1 15 1 x x x x x p (c) ( ) < < < < = 2 1 2 1 3 2 1 0 15 4 0 1 15 1 1 0 x x x x x 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 3. ( ) + + = n n m i n i n m i p 1 , n i ,..., 2 , 1 , 0 = 4. (a) ( ) ( ) 55 1 1 10 2 1 1 10 1 = = + + + = = c c x p x L ( ) ( ) ( )( ) 7 6 1 20 1 10 10 55 1 55 1 10 1 2 10 1 = + + × = = = = = x x x x xp X E ( ) ( ) ( ) 55 4 1 10 10 55 1 55 1 2 2 10 1 3 10 1 2 2 = + × = = = = = x x x x p x X E ( ) 6 7 55 2 = = X Var (b) ( ) 25 12 1 4 1 3 1 2 1 1 1 1 4 1 = = + + + = = c c x p x ( ) ( ) 25 48 1 25 12 4 1 4 1 = × = = = = x x x x x xp X E ( ) ( ) ( ) 5 24 4 3 2 1 25 12 1 25 12 4 1 2 4 1 2 2 = + + + × = × = = = = x x x x x p x X E ( ) 1136 . 1 25 48 5 24 2 = = X Var (c) ( ) ( ) ( ) ( ) ( ) 9 1 1 1 1 1 0 1 1 1 2 2 2 1 1 = = + + + + + = = c c x p x ( ) ( ) ( ) ( ) ( ) ( ) 0 1 1 1 1 0 0 1 1 1 9 1 2 2 2 1 1 = + × + + × + + × = = = x x xp X E
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