rec05-1 - alternative assumptions: (1) after an...

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Massachusetts Institute of Technology 6.041/6.431: Probabilistic Systems Analysis (Fall 2008) Recitation 5 September 18, 2008 1. Problem 2.22, page 123 in the text. Two coins are simultaneously tossed until one of them comes up a head and the other a tail. The Frst coin comes up a head with probability p and the second with probability q . All tosses are assumed independent. (a) ±ind the PM±, the expected value, and the variance of the number of tosses. (b) What is the probability that the last toss of the Frst coin is a head? 2. Problem 2.7, page 120 in the text. You just rented a large house and the realtor gave you 5 keys, one for each of the 5 doors of the house. Unfortunately, all keys look identical, so to open the front door, you try them at random. (a) ±ind the PM± of the number of trials you will need to open the door, under the following
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Unformatted text preview: alternative assumptions: (1) after an unsuccessful trial, you mark the corresponding key, so that you never try it again, and (2) at each trial you are equally likely to choose any key. (b) Repeat part (a) for the case where the realtor gave you an extra duplicate key for each of the 5 doors. 3. Problem 2.20, page 123 in the text. As an advertising campaign, a chocolate factory places golden tickets in some of its candy bars, with the promise that a golden ticket is worth a trip through the chocolate factory, and all the chocolate you can eat for life. If the probability of Fnding a golden ticket is p , Fnd the mean and the variance of the number of candy bars you need to eat to Fnd a ticket. Published September 16, 2008 Page 1 of 1...
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