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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The number of customers arriving per hour at a certain automobile service facility is assumed to follow a Poisson distribution with mean λ = 7. (a) Compute the probability that more than 12 customers will arrive in a 2-hour period. (b) What is the mean number of arrivals during a 2-hour period.
Consider a Poisson distribution with a mean of two occurrences per time period. Compute the probability of three occurrences in one time period (to 4 decimals). Compute the probability of seven occurrences in two time periods (to 4 decimals).
Consider data 5,1,3,5,5,4,3,2 of the Poisson distribution with expectation u. We want to test H0:u=u0 with u0=2. Write the log-likelihood for the data under H0 and the likelihood ratio A(y) for testing H0
The number of forklift topples in an area follows a poisson-process with rate 3 accidents per week. Suppose that we observed one forklift topple in the first week. What is the probability that we will observe at most one forklift topples in the next 2 days?
Let X be a random variable with a uniform distribution over the interval [-6,5]. Compute P(X > -0.4) (The answer should be a number rounded to five decimal places, don't use symbols such as % Compute Fx(-2.2). (The answer should be a number rounded to five decimal places, don't use symbols such as
X is a normally normally distributed variable with mean u =10 and standard deviation a =4. Find A) P(x 1) C) P(10
The Poisson distribution gives the probability for the number of occurrences for a "rare" event. Now, let x be a random variable that represents the waiting time between rare events. Using some mathematics, it can be shown that x has an exponential distribution. Let x > 0 be a random variable and let β > 0 be a constant. Then y = 1 β e−x/β is a curve representing the exponential distribution. Areas under this curve give us exponential probabilities. If a and b are any numbers such that 0 < a < b, then using some extra mathematics, it can be shown that the area under the curve above the interval [a, b] is the following. P(a < x < b) = e−a/β − e−b/β Notice that by definition, x cannot be negative, so, P(x < 0) = 0. The random variable x is called an exponential random variable. Using some more mathematics, it can be shown that the mean and standard deviation of x are the following. μ = β and σ = β Note: The number e = 2.71828 is used throughout…
Officer Thompson of the Bay Ridge Police Department works the graveyard shift. He averages 4.5calls per shift from this dispatcher. Assume the number of calls follows a Poisson distribution. Find theprobability that Officer Thompson get fewer than 2 calls in a shift.
Suppose that Y has an exponential distribution with mean Beta. Show that 2Y/Beta has a chi square distribution with 2 degrees of freedom.
The occurrence of traffic accidents at an intersection may be modeled as a Poisson process. Based on historical records the average rate of accidents is once every 6 years. Part 1 What is the probability that there will be no accidents at the intersection for a period of 3 years? (Answer correct to 3 decimal places.) number (rtol=0.001, atol=D0.001) Part 2 Suppose that in every accident at the intersection, there is a 5% probability of fatality. Based on the above Poisson model what is the probability of one traffic fatality at this intersection in a period of 3 years? (Answer correct to 3 decimal places.) Hint: Note that here you need to find the mean rate of fatalities per year, first. number (rtol=0.001, atol=D0.001)
I have a probability distribution consisting of (x, p(x)): (-3, 0.1), (-2, 0.2), (-1, 0.3), (0, 0.05). The probabilities obviously do not sum to 1. How do I find <x> (average), <x2> (the second moment), <sigmax2> (the variance)?
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…

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