The number of cars that pass through a toll booth on a given highwaybetween 7 and 8 am is distributed Poisson with parameter 15. Each carthat passes through the toll booth may or may not be registered and thisrecord is independent of previous records. The probability of beingregistered is 1/4. Find the joint moment-generating function of thenumber of registered cars and the number of cars that are not registered.

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Answered: The number of cars that pass through a…

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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The number of passengers willing to travel with a certain train is as- sumed to be a Poisson variabel with parameter µ = 300. How many seats should the train have if the probability for an over-booked train should be at most 1%?
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Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a Poisson distribution with parameter μ = 20 (suggested in article "Dynamic Ride Sharing: Theory and Practice," J. of Transp. Engr., 1997: 308-312). What is the probability that the number of drivers will: (i) Be at most 10? (ii) Exceed 20? (iii) Be between 10 and 20, inclusive? (iv) Be strictly between 10 and 20?
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Consider the previous question above, A further study determined that cars arrive to this shopping center according to a non-stationary Poisson process. The mean arrival rate increases linearly from 0.17 to 0.49 cars per minute between 10 am and 2 pm. Then the rate remains constant at 0.49 cars per minute between 2 pm and 4 pm. Finally, the rate changes to a constant 0.33 cars per minute between 4 pm and 5 pm. What is the probability that 60 cars will arrive between 1:45 pm and 4:15 pm?
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Suppose small aircraft arrive at a certain airport according to a Poisson process with rate per hour (alpha = 8), so that the number of arrivals during a time period of t hours is a Poisson rv with parameter (u = 8t) . a. What is the probability that exactly 6 small aircraft arrive during a 1-hour period? At least 6? At least 10? b. What are the expected value and standard deviation of the number of small aircraft that arrive during a 90-min period? c. What is the probability that at least 20 small aircraft arrive during a 2.5-hour period? That at most 10 arrive during this period?
The average demand on a factory store for a certain electric motor is 8 per week. When the storeman places an order for these motors, delivery takes one week. If the demand for motors has a Poisson distribution, how low can the storeman allow his stock to fall before ordering a new supply if he wants to be at least 95% sure of meeting all requirements while waiting for his new supply to arrive?
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The number of bacteria colonies of a certain type in samples of polluted water has a Poisson distribution with a mean of 2 per cubic centimeter (cm3) a. If four 1-cm3 samples are independently selected from this water, find the probability that at least one sample will contain one or more bacteria colonies. b. How many 1-cm3 samples should be selected in order to have a probability of approximately 0.95 of seeing at least one bacteria colony?
Let X1, X2, ... Xn random variables be independent random variables with a Poisson distribution whose parameters are l1, l2, ... ln, respectively. Which of the following is the moment generating function of the random variable Z defined as (the little image)?
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