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 time between successive calls to a corporate office is exponentially distributed with a mean of 10 minutes. Assume that the times between successive calls are independent of each other. Thus, the calls arrive according to a Poisson process. Determine x such that the probability that there are no calls within x minutes is 0.005.
.ll T-Mobile LTE 10:30 PM 1 85% Done 2 of 3 M O FDU O a O FDU FOU FOU O udent.desmos.com/activitybuilder/student/607e171508264d0cbdf6f178#screenldx=5 XM XM w w w FOU FOU se Connec. Clara Destiny sho. O Employment Center + Login Session Expiration. b Selling Associate-. A Sign in P View Portralt Pro. sson 9: Variability in Samples O Nursing Variability of Sample Estimates Estimates for population characteristics are usually given along with a margin of error. The margin of error is the maximum expected difference between the estimate of the population characteristic and the actual population characteristic. Each of the sample proportions are good estimates of the population proportion, so we should give a margin of error that contains about 95% of the sample proportions to be reasonably sure that the actual population proportion is in the range between the mean minus the margin of error to the mean plus the margin of error. What margin of error should be given along with the estimate of…
. Find the moment generating function about origin of the Poisson distribution.
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A burger joint has on average 9 customers arriving per hour. There is only one employee serving customers and she takes about 4 minutes on average to serve a customer. The burger joint is open 10 hours per day and makes a profit of $10 for each burger sold. The staff has a pay rate of $20/hour. Assume a Poisson distribution on the arrival rate of customers and exponential distribution on the service time of the employee. Q. If customers do not want to spend more than 6 minutes in the burger joint (including waiting and service), how much potential profit would the joint lose per day?
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Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…
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