Generalize Exercise 5.4-3 by showing that the sum of n independent Poisson random variables with respective means

Question:

Generalize Exercise 5.4-3 by showing that the sum of n independent Poisson random variables with respective means μ1, μ2, . . . , μn is Poisson with mean
μ1 + μ2 + · · · + μn.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Probability and Statistical Inference

ISBN: 978-0321923271

9th edition

Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

See More Books

Question Posted: Oct 12, 2015 08:50 AM

See More Questions

Suppose that Xi, i = 1, 2, 3 are independent Poisson random variables with respective means i, i = 1, 2, 3. Let X = X1 + X2 and Y = X2 + X3. The random vector X, Y is said to have a bivariate Poisson...
Consider X 1 , X 2 , ., X n independent Poisson random variables with parameters 1 , 2 , , n. Use the properties of moment-generating functions to show n that the random variable n i = 1 Xi is...
Let X1, . . . ,X20 be independent Poisson random variables with mean 1. (a) Use the Markov inequality to obtain a bound on (b) Use the central limit theorem to approximate 20 , > 15
Three components can be used to build an Oracle statement: Statement, Prepared-Statement and CallableStatement.(True/False)
1. What actions should be taken in order to increase the morale and motivation level of the clerical staff at the Rutledge Company? 2. What actions can be taken to motivate those employees who are...
How successful are government contracting arrangements? How do these compare, for instance, with the arrangements BAA had with their suppliers in the construction of T5 at Heathrow (Project...
How do sequence diagrams for design differ from those for analysis? In which one do boundary objects appear? Why?
The financial statements of Marks and Spencer plc (M&S) are available at the books companion website or can be accessed at corporate.marksandspencer...
Sage Hill Company purchased a delivery truck (vehicles) on June 1 for $38,520, paying $18,600 cash and signing a 5%, two-month note for the remaining balance, interest to be paid at maturity. The...
Lab Exercise -- C++ Structures Objective: The purpose of the program is to: 1. Write functions to read in and print an Employee struct 2. Write an additional function that passes in an array of...
Let X1 and X2 be two independent random variables. Let X1 and Y = X1 + X2 be 2(r1) and 2(r), respectively, where r1 < r. (a) Find the mgf of X2. (b) What is its distribution?
Let X1, X2, X3, X4, X5 be a random sample of size 5 from a geometric distribution with p = 1/3. (a) Find the mgf of Y = X1 + X2 + X3 + X4 + X5. (b) How is Y distributed?
Nestl Group, a multinational food products firm based in Switzerland, recently issued its financial statements. The auditors opinion attached to the financial statements stated the following: In our...
Prepaid college tuition plans, also known as Prepaid Education Arrangements (PEAs), allow you to prepay college tuition at present-day prices. The value of the investment is guaranteed by the state...
In 2005, a federal court authorized United Airlines (UAL) to terminate its pension plan. The government will take over pension payments to retired UAL employees, but this action means that pension...
Is the following statement true, false, or uncertain? Why? If a married womans husband gets a raise, she tends to work less, but if she gets a raise, she tends to work more.
The marginal revenue product of labor at the local sawmill is , where L = the number of workers. If the wage of sawmill workers is $10 per hour, then how many workers will the mill hire? MRP 20 0.5L,...
Many crimes against property (burglary, for example) can be thought of as acts that have immediate gains but run the risk of long-run costs. If imprisoned, the criminal loses income from both...
Find a general term a n for the geometric sequence with a 1 = 2.5 and a 6 = -80.
Anne is employed by Bradley Contracting Company. Bradley has a $1.3 million contract to build a small group of outbuildings in a national park. Anne alleges that Bradley Contracting has discriminated...
P (A1) 5 .60, P (A2) 5 .40, P(B1A1) 5 .05, and P(B1A2) 5 .10. Use Bayes theorem to determine P (A1B1).
The Ludlow Wildcats baseball team, a minor league team in the Cleveland Indians organization, plays 70% of their games at night and 30% during the day. The team wins 50% of their night games and 90%...
Dr. Stallter has been teaching basic statistics for many years. She knows that 80% of the students will complete the assigned problems. She has also determined that among those who do their...
Q1) Find expressions for the Revenue, Cost, and Profit from selling x thousand items. Item Price Variable Cost $8.00 3816x Fixed Cost $71,174
1. There are many market disruptions in the news today. (If you get stuck, on the last slide of the PowerPoint, I've given you 2 examples.) Choose any disruptor in the news and, (a) summarize the...
Discuss at least five of the formatting decisions you would have to make when typing a table. Compare the decisions you provided to those of two of your classmates. Do you agree or disagree with the...

Generalize Exercise 5.4-3 by showing that the sum of n independent Poisson random variables with respective means

Question:

Step by Step Answer:

The moment generating ...View the full answer

Probability and Statistical Inference

Students also viewed these Statistics questions