hw8sol_fall03 - AMS 310.01 FALL 2003 Homework#8 Solutions...

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Unformatted text preview: AMS 310.01 FALL 2003 Homework #8 Solutions 2.48 Let i i x cu a = + . Then 1 1 1 1 ( ) n n n i i i i i i x u na x cu a c cu a n n n n = = = = = + = + = + Now, 2 2 2 2 2 2 2 2 1 1 1 1 ( ) ( ) ( ) ( ) ( 1) ( 1) ( 1) ( 1) n n n n i i i i x u i i i i x x cu a cu a cu cu u u s c c s n n n n = = = =- +---- = = = = =---- Thus, x u s c s = 5.72 (a) The independent random variables 1 2 and X X have the same probability distribution ( ;2,0.3) b x . Hence the joint probability distribution of 1 2 and X X is 1 2 1 2 ( , ) ( ;2,0.3) ( ;2,0.3) f x x b x b x = 1 1 2 2 1 2 1 2 2 2 4 1 2 1 2 2 2 2 2 (0.3) (0.7) (0.3) (0.7) (0.3) (0.7) x x x x x x x x x x x x-- +-- = = where 1 2 0,1,2, and 0,1,2. x x = = (b) 1 2 ( ) (0,1) (0,2) (1,2) P X X f f f < = + + 1 3 2 2 3 1 2 2 2 2 2 2 (0.3) (0.7) (0.3) (0.7) (0.3) (0.7) 1 2 1 2 = + + = 0.2058 + 0.0441 + 0.0378 = 0.2877 = 0....
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This homework help was uploaded on 01/31/2008 for the course AMS 310.01 taught by Professor Mendell during the Fall '03 term at SUNY Stony Brook.

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hw8sol_fall03 - AMS 310.01 FALL 2003 Homework#8 Solutions...

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