Let, Xi (t) i 1, 2 n, be a sequence of independent Poisson counting processes with arrival rates,i Show that the sum of all of these Poisson processes, Is itself a Poisson process What is the arrival rate of the sum process X(t) X,(t), i 1 1 1

Question: Let, Xi (t) i = 1, 2 n, be a sequence of independent Poisson counting processes with arrival rates,i. Show that the sum of all

Let, Xi (t) i = 1, 2€¦ n, be a sequence of independent Poisson counting processes with arrival rates,Î»i. Show that the sum of all of these Poisson processes,

Is itself a Poisson process. What is the arrival rate of the sum process?

X(t) = X,(t), i = 1 1-1

Step by Step Solution

★★★★★

3.48 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Using probability generating functions Defin... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

589-M-S-C-R-V (1236).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let X1, . . ., Xn be a sequence of independent Poisson-distributed random variables, with parameter . Let Show that S,=E-X- i=l-

Let X1, X2¦ X5 be a sequence of five independent discrete random variables, each with a distribution described by: (a) Find the probability mass function of the median (third largest) of these...

Let Xk, k = 1, 2, 3¦ be a sequence of IID random variables with finite mean, , and let Sn be the sequence of sample means, (a) Show that the characteristic function of Sn can be written as (b)...

Submitted to Management Science manuscript MS-0001-1922.65 Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title....

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

Using "On the Spectrum of Hydrogen" by Niels Bohr -What is the main idea of the Author's argument? What is the main essence of the piece? -What ways does the author use to propose and support their...

Please help me with my macro quiz Problem 2: A two-server queueing system is in a steady-state condition and the steady state probabilities are po = 16: P1 = 16 : P2 = 16:P3 = 16 . PA = 16: Pn = 0 if...

Help with the following math problems 1. The table below shows data for a life insurance portfolio in which the lives are independent with respect to mortality. Mortality rate Sum assured Number of...

1.4 Sum of Poisson 1. Let X and Y be independent r.v.s, both are Poisson distributed with parameter respectively and M. Compute the distribution of Z = X +Y. We can recall Newton's formula: " n n...

Please help me tackle the following question. Thanks The random variable S represents the annual aggregate claims for an insurer from policies covering damage due to windstorms. S is modelled as...

On Thursday, 4th June 2020, a group of students from University of Ghana Business School (UGBS) and the Department of Political Science were debating whether Management should be classified as a...

The following section is taken from Centralia Oil Company's balance sheet at December 31, 2011. Interest is payable annually on January 1. The bonds are callable on any annual interest date....

Now suppose Terry joins a risk sharing arrangement with other small business owners and now a total of 1 8 buildings are in the risk sharing pool.Assume that the property losses for the additional...

Develop a personality test aimed at measuring these dimensions. Make sure that each dimension you want to measure is captured by at least ve questions.

A buyer for a large department store chain must place orders with an athletic shoe manufacturer six months prior to the time the shoes will be sold in the department stores. In particular, the buyer...

Each day the manager of a local bookstore must decide how many copies of the community newspaper to order for sale in her shop. She must pay the newspapers publisher $0.40 for each copy, and she...

Two construction companies are bidding against one another for the right to construct a new community center building in Bloomington, Indiana. The first construction company, Fine Line Homes,...

A simple random sample from a population with a normal distribution of 105 body temperatures has x = 98.90"F and s =0.63"F. Construct a 90% confidence interval estimate of the standard deviation of...

What is the future value of $1,100 placed in a savings account for four years if the account pays 8.00% compounded quarterly?

Butler International Limited is evaluating a project in Erewhon. The project will create the following cash flows: Year Cash Flow 0 $ 950,000 1 285,000 2 345,000 3 415,000 4 255,000 All cash flows...