11ProbHw4 - IEOR 3658 Probability Prof Mariana...

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IEOR 3658 Assignment #4 Probability October 4, 2011 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #4 – due October 12th, 2008 1. The annual premium of a special kind of insurance starts at $1000 and is reduced by 10% after each year where no claim has been filed. The probability that a claim is filed in a given year is 0.05, independently of preceding years. What is the PMF of the total premium paid up to and including the year when the first claim is filed? 2. (From text) The Columbia soccer team has 2 games scheduled for one weekend. It has a 0.4 probability of not losing the first game, and a 0.7 probability of not losing the second game, independently of the first. If it does not lose a particular game, the team is equally likely to win or tie, independently of what happens in the other game. The Columbia team will receive 2 points for a win, 1 for a tie, and 0 for a loss. Find the PMF of the number of points that the team earns over the weekend.
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