Officer Joe Sixpack of the UConn Police is on patrolling duty Saturday night. He decidesto devote the hour between 11 PM and midnight to catching cars running red lights.The number of cars running the red light at the intersection of CT 195 and NorthEagleville during that hour has a Poisson distribution with mean 0.6, that at theintersection of CT 195 and CT 275 a Poisson distribution with mean 0.5, and that at theintersection of Hillside and North Eagleville a Poisson distribution with mean 0.4.Officer Sixpack finds 6 Blue pens, 4 Black pens, and 2 Red pens in his penholder. Herandomly selects (needless to say, without replacement) 2 pens from his penholder.If he does not get a single Blue pen, he will monitor the intersection of CT 195 and NorthEagleville.If he gets 1 Blue pen, he will monitor the intersection of CT 195 and CT 275.If he gets 2 Blue pens, he will monitor the intersection of Hillside and North Eagleville.If Officer Sixpack returns to his desk after midnight without catching a single car runningthe red light, what is the probability that he monitored the intersection of CT 195 and CT275?

We will use Baye's theorem to solve this problem.Let A denote that Officer Sixpack monitored the…

Answered: Officer Joe Sixpack of the UConn Police…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Each day a hospital records the number of people who come to the emergency room for treatment. In the last week, the observation from Sunday to Saturday are 11, 8, 12, 14, 7, 39, 57. Would you expect the Poisson distribution to better describe, or more poorly describe, the number of weekly admissions to the hospital for a rare disease? Why?
he Princeton Review, a company that tracks information about various colleges, reports that 30% of CofC students are out-of-state students. If we took many samples of CofC students, and for each sample calculate the proportion $\hat{p}$ of out-of-state students in that sample, what would be the center of this distribution?
An insurance company has a policy which insures a house against fire. The records of one particular period of 30 days yielded the following results. C. Number of claims 1 2 3 4 5 or more No of days 8 11 4 1 i. Fit a Poisson distribution to this data. ii. Calculate the expected frequencies for this Poisson distribution.
The shape of the mean-variance frontier that results from the combination of a riskless and arisky asset is…..:a. Is U-shaped, tilted 90 degrees clockwise.b. Is a straight line passing from the mean-variance points of the two assets.c. Is a hyperbola.d. Consists of two straight lines, each connecting one of the two assets to a risk-freeportfolio
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3. The number of planes landing in a busy airport during 10-minute intervals is thought to have a Poisson distribution. To test this hypothesis 500 trials were recorded. The table shows the number of trials when 0, 1, 2, 3, 4 or more planes landed during each 10-minute interval. Number of planes 0 1 2 3 4 or more Number of trials 408 81 10 1 0 i. Fit a Poisson distribution to the above data. ii. Test the hypothesis that the variable, X 'the number of planes landing in the airport during 10-minute intervals' has a Poisson distribution using a 0.01 level of significance.
A merchant sells on the average 2.3 cakes on a round of his route. Cakes are packaged two to a box but are sold individually. At the end of the round, the salesman eats any cake left over in a box that has been opened. He only opens a box after emptying the previous box. If the number of cakes sold has a Poisson distribution, then on what proportion of rounds does he have a cake to eat? (4 decimal accuracy).
A company buys a policy to insure its revenue in the event of major snowstorms that shut down business. The policy pays nothing for the first such snowstorm of the year and $9300 for each one thereafter, until the end of the year. The number of major snowstorms per year that shut down business has a Poisson distribution with mean 2.8. Find the expected amount paid to the company under this policy during a one-year period.
14. The distribution of the number of road accidents per day in a city is Poisson with a mean of 4. Find the number of days out of 100 days when there will be (i) no accident, (i) at least 2 accidents, and (iii) at most 3 accidents. (3 ( 01 (HD) 447
A restaurant manager is planning a new layout for the tables in his store. He will be placing tables of 2, tables of 4, and tables of 6 throughout the dining room. To help him decide how many of each he needs, he decides to keep track of all table requests by customers during a 2-week period. Which measure of central tendency would BEST indicate the typical table size needed?
7. Suppose the time it takes a data collection operator to fill out an electronic form for a database is uniformly between 1.5 and 2.2 minutes. a. What is the mean and variance of the time it takes an operator to fill out the form? b. What is the probability that it will take less than two minutes to fill out the form? C. Determine the cumulative distribution function of the time it takes to fill out the form.

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