solna2 - Actsc 372 F08: Assignment 2 Solution (Total marks:...

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Unformatted text preview: Actsc 372 F08: Assignment 2 Solution (Total marks: 30) 1. (2 marks each) (a), (b) and (c) E ( A ) = 0 . 3(0 . 123 + 0 . 065 + 0 . 03) = 0 . 0726667 E ( B ) = 0 . 3(- . 037 + 0 . 03 + 0 . 05) = 0 . 0143333 V ar ( A ) = E [ A- E ( A )] 2 = 0 . 00147089 s.d. ( A ) = 0 . 03835 V ar ( B ) = E [ B- E ( B )] 2 = 0 . 00138422 s.d. ( B ) = 0 . 0372 cov ( A,B ) = E [( A- E ( A ))( B- E ( B ))] =- . 00140855555 =- . 00140855555 . 03835 . 0372 =- . 9871 2. (a) (3 marks) Solution 1: 2 P = x 2 1 2 1 + (1- x 1 ) 2 2 2 + 2 x 1 (1- x 1 ) 1 2 2 P x 1 = 2 x 1 2 1- 2(1- x 1 ) 2 2 + (2- 4 x 1 ) 1 2 = 0 x MIN 1 = 2 2- 1 2 2 1 + 2 2- 2 1 2 = 0 . 82 x MIN 2 = 1- x MIN 1 = 0 . 18 x MIN = 0 . 82 1 + 0 . 12 2 = 9 . 08% 2 x MIN = [0 . 82(0 . 15)] 2 + 2(0 . 82)(0 . 18)(0 . 3)(0 . 15)(0 . 25) + [0 . 18(0 . 25)] 2 = 0 . 020475 x MIN = 14 . 309% Solution 2: = . 0225 . 01125 . 01125 . 0625 D = 0 . 0225(0 . 0625)- . 01125...
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This note was uploaded on 09/18/2011 for the course ACTSC 372 taught by Professor Maryhardy during the Winter '09 term at Waterloo.

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solna2 - Actsc 372 F08: Assignment 2 Solution (Total marks:...

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