TP%237_f08 - CE 3102 Fall 2008 Thought Problem 7 Turning...

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Unformatted text preview: CE 3102 Fall 2008 Thought Problem 7 Turning Volumes At an intersection of two one-way streets, vehicles arrive on the northbound approach and can either turn left or go straight through. If a total of n vehicles arrive during a signal cycle, if the probability a given driver turns left is p, and if drivers turning decisions are independent of each other: (a) find the probability distribution over the number of left- turning vehicles; (b) verify that this is a legitimate probability distribution; (c) find the expected value and variance for this distribution when n=20 and p=0.10. CE 3102 Fall 2008 Thought Problem 7 Instructors Partial Solution Lets illustrate the structure of this problem with the case n=3, before we tackle the general case. Let L denote the event a vehicle turns left, and T denote the event a vehicles goes straight through. One possibility is that all vehicles go straight, which we can denote as TTT. The probability a vehicle turns left is p, so the probability it goes straight is (1-p), as TTT....
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TP%237_f08 - CE 3102 Fall 2008 Thought Problem 7 Turning...

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