Stats 134 - Spring 2005 - Pitman - Midterm 1

Stats 134 - Spring 2005 - Pitman - Midterm 1 - Stat 134...

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Unformatted text preview: Stat 134 MIDTERM (Sec 2, Spring 2005) J. Pitman. Name and SID number: You must either show your work or provide brief explanations to obtain full credit. 1. A deck of 4 cards contains one card numbered 0, two cards numbered 1, and one card numbered 2. The deck is shuffled thoroughly. Let T be the sum of the numbers on the top two cards. a) Display the distribution of T in a suitable table. b) Find the expected value of T . c) Find the variance of T . d) Suppose that the shuffling is repeated over and over. For n = 1 , 2 ,... let T n denote the sum of numbers on the top 2 cards after the n th shuffle has been made. Let A n := ( T 1 + T 2 + · · · + T n ) /n which is the average value of T obtained in n repetitions. Find a number x so that P ( A n ≤ x ) is approximately 84%. 2. Consider a sequence of independent trials, each of which results in a success with probability p , a failure with probability q , and no result with probability r , where p + q + r = 1....
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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.

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Stats 134 - Spring 2005 - Pitman - Midterm 1 - Stat 134...

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