Let X have a Poisson distribution with Ax = 2. Let Y have a Poisson distribution with Ay = 3.Suppose that X and Y are independent.Show (prove) that the sum X + Y has a Poisson distribution with parameter 5.Compute P(X + Y ≥ 2), the probability that the sum is greater than or equal to 2.You can assume that the sum has a Poisson distribution with parameter 5.Please upload a file with your work (you can upload the same file for all parts of this problem).

Let have a Poisson distribution with . and Let have a Poisson distribution with .The PMF of of…

Answered: Let X have a Poisson distribution with…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
A hotel has 50 "luxury" rooms and 250 "regular" rooms. On a given night, the demand for luxury rooms is Poisson distributed with mean 45, and the demand for regular rooms is Poisson distributed with mean 270. If the demand for regular rooms exceeds 250, each person who wants a regular room but can't get one is willing, with probability 0.3, to upgrade to a luxury room if any luxury rooms are still available. After running a simulation with at least 5,000 replications, what is the most realistic conclusion about the probability that all 300 rooms will be occupied? a. This probability is around 0.21. b. This probability is around 0.54. c. This probability is around 0.32. d. This probability is around 0.68.
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In the first hour of customers using the app they served 180 customers. STACO decided to treat this hour as 60 non-overlapping intervals of one minute each. They then assumed they could model the number of customers served each minute by independent and identically distributed Poisson Random Variables. They called the number of customers served in the ith minute X₁, so X₁ + X₂ + ... + X60 180, X₁~ Poisson(X), and X; and X, are independent if i j. - STACO used this to compute an estimated 95% confidence interval and then told Coffee Kart that they could claim to serve an average of three customers per minute. = i Recall that the maximum likelihood estimator of A is A X. Using the same assumptions as STACO and assuming that n is large enough to apply the Central Limit Theorem, calculate an estimated 95% confidence interval for X. ii Do you agree with the assumptions made by STACO. Justify your answer.
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5
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Town Taxi uses three dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to Town Taxi use a common number. When all dispatchers are busy, the caller hears a waiting song until the first dispatchers becomes available. The telephone system will assign available dispatcher to the waiting callers according to FCFS. Assume that the arrival of calls follows a Poisson distribution, with an average of 35 calls per hour. Also assume that the time that each dispatcher spends with a customer follows Exponential distribution and each dispatcher takes an average of 3 minutes with each caller. a What percentage of time all dispatchers are idle? b What percentage of time only one dispatcher is busy? c. What is the average number of callers in the system? d What is the average time in minutes that a customer spends in the system? e What is the total cost of the system for 8 hours if each dispatcher charges $25 /hour and the waiting cost per hour for…
An automobile manufacturer has developed a new type of bumper, which is supposed to absorb impacts with less damage than previous bumpers. The manufacturer has used this bumper in a sequence of 25 controlled crashes against a wall, each at 10 mph, using one of its compact car models. Let X = the number of crashes that result in no visible damage to the automobile. 1.The (parameter/random_variable/statistics/variable) , [variable],[statistics],[random_variable] to be estimated is p. 2. Continuing this question, p the is (percentage/median/average/poportion) of such crushes that result in no damage [alternatively, p = P(no damage in a single crash)]. Select the correct answer from the options inside the (bracket).

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