20061ee131A_1_131A6

20061ee131A_1_131A6 - success being a call in each...

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EE 131A Homework #6 Winter 2006 Due March 2rd K. Yao Read Leon-Garcia, pp. 191–221 1. Problem 51, page 179. 2. Problem 54, page 180. 3. Problem 57, page 180. 4. Problem 59, page 181. 5. Consider the application of the Poisson distribution to the evaluation of arrival prob- lems in a telephone system. Let λ denote the average number of calls per unit time (also called the arrival rate). Assume the calls arrival independently. Then the proba- bility of the number of calls per unit time is modeled by the Poisson distribution with λ given by the arrival rate. This result follows from the approximation of the Binomial distribution by the Poisson distribution. Specifically, divide each unit time into a large number n of smaller intervals, so that for a small enough interval, there is either 0 or at most 1 call in that interval. Then these n time intervals are Bernoulli trials with
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Unformatted text preview: success being a call in each interval. We do not know n or p but we do know = np . Thus, k calls per unit time is given by e- k /k !. Now, suppose we know on the average there are 2 calls per second. Find the probability of having at most 3 calls in 5 seconds. (Hint: Find the average number of arrivals in 5 seconds.) 6. We buy cylinders with a diameter of 2 and is willing to accept diameters that are o by as much as . 05. The factory produces a diameter that is normally distributed with = 2. (a). If = 0 . 08, what percentage will be rejected by us? (b). If the rejection rate is 20%, nd . 7. Problem 65, page 181. 8. Problem 67, page 181. 9. Problem 72, page 181....
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This note was uploaded on 06/09/2010 for the course EE 131A taught by Professor Lorenzelli during the Spring '08 term at UCLA.

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