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Unformatted text preview: Statistics 20: Quiz 3 Solutions 1. Suppose X 1 ,...,X 64 are independent copies of X N (0 , 2 2 ). Find SD ( X ). With n = 64, SD ( X ) = SD ( X i ) n = 2 64 = 1 4 . 2. You design a strategy for playing Black Jack so that in each game you expect to win 5 dollars with a standard deviation of 10 dollars. You quit your day job and vow to play professionally; under reasonable assumptions, you can easily play 10 , 000 independent games of Black Jack at casinos in the next 6 months. What is the probability that you win more than 51 , 000 dollars doing so? With n = 10 , 000, let X 1 ,...,X n denote the winnings (which may be positive, negative, or zero) on the i th game of Black Jack. We are interested in the total winnings X = n X i =1 X i . By the CLT, X has an approximately Normal distribution. We need to determine its expected value and standard deviation: E [ X ] = nE [ X i ] = (10 , 000)5 = 50 , 000; SD ( X ) = nSD ( X i ) = 10 , 000(10) = 1000....
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This note was uploaded on 04/02/2008 for the course STAT 20 taught by Professor Staff during the Spring '08 term at University of California, Berkeley.
- Spring '08