final07 - MS&E 120 Probabilistic Analysis Handout #11,...

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Unformatted text preview: MS&E 120 Probabilistic Analysis Handout #11, Page 1 of 4 Autumn 2007 Prof. Ross D. Shachter Final Examination December 12, 2007 MS&E 120: Probabilistic Analysis Final Examination Three Hours. You will lose credit if you do not turn in your work when time expires. Open book. You may freely use your book, notes, and handouts from this quarters course. Read and sign the honor code on your blue book(s) or we will not grade your exam. This examination tests your individual knowledge. No collaboration is permitted. Be careful to budget your time. All questions will be weighted equally and all parts of each question will be weighted more or less equally, so you should not waste time on parts you find more difficult until you have completed easier parts. No calculators or computers are permitted at the examination. Calculations will be kept as simple as possible. You can receive all of the credit for setting up the correct result even if you do not perform all of the calculations. Please start each question on a new page and label the parts clearly. Partial credit will be given whenever possible, provided your solution is neat and clear. Someone will be outside the room if you have any questions. Good Luck and Clear Insights! Please do not open the examination until everyone is ready and you are asked to begin. MS&E 120 Probabilistic Analysis Handout #11, Page 2 of 4 Autumn 2007 Prof. Ross D. Shachter Final Examination December 12, 2007 1. Sticky wickets The uncertainty scholars are engaged in a tournament of a game they call crickets, where Debarun believes that the time in days spent on each game is described by a Uniform ( 2, 8 ) random variable. He believes that the outcome of each game is independent and that he has a 75% chance of winning against Caleb and 80% against Kihoon. a) If Debarun only plays against Caleb, find the expected value and variance of the number of games they will play until Debarun wins his first game. b) Find the expected value and variance of the number of days for each game. c) If Debarun only plays against Caleb, find the expected value and variance of the number of days they will play until Debarun wins his first game....
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This note was uploaded on 10/14/2008 for the course MS&E 120 taught by Professor Shatcher during the Fall '08 term at Stanford.

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final07 - MS&E 120 Probabilistic Analysis Handout #11,...

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