Question: There is an interesting relationship between negative binomial and gamma random variables, which may sometimes provide a useful approximation. Let Y be a negative binomial

There is an interesting relationship between negative binomial and gamma random variables, which may sometimes provide a useful approximation. Let Y be a negative binomial random variable with parameters r and p, where p is the success probability. Show that as p → 0, the mgf of the random variable pY converges to that of a gamma with parameters r and 1.

Step by Step Solution

★★★★★

3.35 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

If Y negative binomialr p its moment generating function is ... 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)

941-M-S-P (8598).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let X be a binomial random variable with parameters n and p. Show that p)n+ n + Dp

Philanthropic organizations often rely on contributions from individuals to finance the work that they do, and a national veterans organization is no exception. The Paralyzed Veterans of America...

There is an interesting connection between the Creasy-Williams confidence set of (12.2.24) and the interval CG() of (12.2.22). (a) Show that where is the MLE of Î² and 2Î² is...

These questions were rendered in R markdown through RStudio ( , ). Please complete the following tasks regarding the data in R. Please generate a solution document in R markdown and upload the .Rmd...

Possible Multiple Choice Questions for the Exam. Focus on the topics discussed in class. Chapter 1 Multiple Choice Identify the choice that best completes the statement or answers the question. ____...

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

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...

Instuctor's Annotated Edition TENTH EDITION Understandable Statistics Concepts and Methods Charles Henry Brase Regis University Corrinne Pellillo Brase Arapahoe Community College Australia Brazil...

Set Student Name: 1. Describe the relationship between two variables that have a correlation coefficient value: a. Near -1 b. Near 0 c. Near 1 2. Data was collected where a weightlifter was asked to...

Set Student Name: 1. Answer true or false for each part, and if false, explain your answer. a. The point estimate for the population mean, , of an x distribution is x-bar, computed from a random...

Economics A new machine comes with 180 free service hours over the first year. Additional time costs $176.1 per hour. What is the margi Fifty years ago, Jessy purchased a set of silver-plated...

Find the exact value of the expression below. (9) 3/2 (6) 12/Q (C0, d) 1 (4) Undefined. 2) find the missing Coordinate of the point, given that the point is in quadrant I. ( 5/161) -5 (61 (9) 5/6 (b)...

When you buy a product on eBay you can pay for it using an online payment system called PayPal ( which accepts credit cards or electronic funds transfers ) . PayPal represents a ( n ) _ _ _ _ _ _ _ _...

Consider equations (1.1) and (1.3) together as a model of GDP and consumption. Algebraically and graphically (modifying Figure 1.2 as needed), analyze separately the counterfactual experiments of (a)...

A computer center recorded the number of programs it maintained during each of 10 consecutive years. Year Number of Programs 1 ........ 430 2 ........ 480 3 ........ 565 4 ........ 790 5 ........ 885...

By the method of least squares, fit the regression plane y = 1 + 2x1 + 3x2 to the following 12 observations of (x1, x2, y): (1, 1, 6), (0, 2, 3), (3, 0, 10), (2, 0, 4), (1, 2, 0), (0, 0, 1), (2, 1,...

Consider the following 16 observed values, rounded to the nearest tenth, from the exponential distribution that was given in this section: (a) Take re-samples of size n = 16 from these observations...

The Lopez-Portillo Company has $11.3 million in assets, 90 percent financed by debt, and 10 percent financed by common stock. The interest rate on the debt is 10 percent and the par value of the...

Daily Enterprises is purchasing a $ 1 4 , 0 0 0 , 0 0 0 machine. The machine will depreciated using straight - line depreciation over its 6 year life and will have no salvage value. The machine will...

Assume the following rates are being utilized for the given yearly periods. Assume the following rates are being utilized for the given yearly periods. I = 8% for 0 lessthanorequalto t