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Unformatted text preview: Stat 134 MIDTERM (Sec 1, Fall 2004) J. Pitman. Name and SID number: 1. Let X 1 ,X 2 ,X 3 ,... represent the numbers obtained on random draws with replacement from a box of 4 tickets numbered 0 , 1 , 1 and 2. a) Display the distribution of X 1 + X 2 in a suitable table. b) Identify this distribution as a standard one, and indicate its parameters. c) Obtain decimal values for the mean and variance of this distribution. d) Give a numerical expression for P ( X 1 + X 2 = X 3 + X 4 ) e) Let P = P ( X 1 + X 2 + · · · + X 49 + X 50 ≤ 55). Find z such that P differs from Φ( z ) by at most 0 . 01, where Φ is the standard normal cumulative distribution function. 2. In a kids’ baseball league, teams A and B play until one team has won two games. Assume that each game played is won by team A with probability p A , independently of the results of all previous games. Let G be the number of games played, and G A the number of games won by team A . a) Give a formula in terms of p A for P ( G A...
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This note was uploaded on 02/06/2012 for the course STATISTICS 134 taught by Professor Shobhana during the Fall '11 term at University of California, Berkeley.
- Fall '11