180asolns3 - 180A HW 3 Solutions October 25, 2006 1) On a...

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Unformatted text preview: 180A HW 3 Solutions October 25, 2006 1) On a multiple-choice quiz with 3 possible answers for each of the 10 questions, what is the expected number of correct answers a student would get just by guessing? Answer Let X denote the number of correct answers guessed. Then note that X Bin (10 , 3) so E [ X ] = 10 / 3 . 2) Two marbles a drawn without replacement from a box that contains 5 red and 5 blue marbles. If they match you win $1 . 10 ; otherwise, you lose $1 . 00 . Calculate the expected value and the standard deviation of the amount you win. Answer Let X denote our winnings, in dollars. We note that P ( X = 1 . 1) = P ( 2 Red Drawn ) + P ( 2 Blue Drawn ) = 2 ( 5 2 )( 5 ) ( 10 2 ) = 2 10 45 = 4 9 . Furthermore P ( X =- 1) = 1- P ( X = 1 . 1) = 5 / 9 (as these are the only two values X can take). Thus, we note that E [ X ] =- 1 P ( X =- 1) + 1 . 1 P ( X = 1 . 1) =- 5 9 + (1 . 1) 4 9 =- 50 90 + 44 90 =- 6 90 We note that E [ X 2 ] = (- 1) 2 P ( X =- 1) + (1 . 1) 2 P ( X = 1) = 500 900 + 484 900 = 984 900 Finally we note that SD ( X ) = p V ar ( X ) = p E [ X 2 ]- ( E [ X ]) 2 = r 984 900- 60 900 = r 924 900 3) Jim and Sara play Rock, Paper, Scissors . Assume each round both Jim and Sara choose among rock, paper and scissors with equal probability. (a) What are the chances that the game ends on the sixth round?...
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This note was uploaded on 02/03/2008 for the course MATH MATH 180A taught by Professor Castro during the Fall '08 term at UCSD.

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180asolns3 - 180A HW 3 Solutions October 25, 2006 1) On a...

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