Question: Show that, after making the substitution p = /n, the binomial mgf converges to the Poisson mgf as n .

Show that, after making the substitution p = /n, the binomial mgf

Show that, after making the substitution p = /n, the binomial mgf converges to the Poisson mgf as n .

Step by Step Solution

★★★★★

3.54 Rating (161 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

The binomial momentgenerating function ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

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

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

1.8 List and describe two key areas of organisational policies and procedures for financial administration relating to budgeting, e.g. reporting, recordkeeping, accuracy of data, historical records...

Q:

The binomial random variable, x, may be used as the test statistic when testing hypotheses about the binomial parameter, p.When n is small (say, 15 or less), Table 2 in Appendix B provides the...

Q:

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...

Q:

Use the mgfs to show that the binomial distribution converges to the Poisson distribution. The convergence is taken so that pn > 0. (Write the p in the binomial distribution as /n.)

Q:

A worker pushes a wheelbarrow with a horizontal force of 50 N on level ground over a distance of 5.0 m. If a friction force of 43 N acts on the wheelbarrow in a direction .What work will be done on...

Q:

Please ASAP and start from e Problem 5 Here, we will be deriving mof's of some of our brand name r.v.'s and using them to prove cool things about distribution theory. (a) [harder] Using the...

Q:

MATH S350 TMA 01 Hints Question 1 Let A and B be the event that water is contaminated with excessive amount of pollutant A and pollutatnt B respectively. Remarks: 1. Half of those communities whose...

Q:

Show that the binomial moment generating function converges to the Poisson moment generating function if we let n and p 0 in such a way that np approaches a value > 0. There is in fact a theorem...

Q:

109. Show that the binomial moment generating function converges to the Poisson moment generating function if we let nSqand pS0 in such a way that np approaches a value l 0. [Hint: Use the calculus...

Q:

In this question, you will use the MGF to show that the binomial distribution converges to the Poisson distribution as n goes to infinity. (a) (3 pts) Y1, ..., Yn are iid Poisson distributed random...

Q:

2. (10pts) In this question, you will use the MGF to show that the binomial distribution converges to the Poisson distribution as n goes to infinity. (a) (3 pts) Yl, ..., Yn are iid Poisson...

Q:

A company has total assets of $653 million and total liabilities of $367 million. If the company has 36 million shares outstanding that are currently priced at $47.23 per share, what is the firm's...

Q:

The main objective of estate planning is to save lawyers fees. true false

Q:

Find the exact slope of the tangent line to the parametric curve x = 4 c o s ( t ) y = 2 s i n ( t ) at the point where t = 3 . Give an exact answer, do not use a decimal.

Q:

On January 1, 2015, Company P sold a machine to its 70%-owned subsidiary, Company S, for $60,000. The book value of the machine was $50,000. The machine was depreciated using the straight-line method...

Q:

Compare and contrast the truckload segment of the motor carrier industry with the LTL segment in terms of infrastructure, cost structure, market structure, and operating characteristics.

Q:

Jim O'Brien has realized for quite some time that some of Hardee's customers are more profitable than others. This is also quite true for certain freight lanes. However, Hardee has traditionally...

Q:

Widgets are produced by a constant-cost industry. Suppose the government decides to institute an annual subsidy of $8,000 per year to every firm that produces widgets. a. Explain why, in the long...

Q:

Your firm has been engaged to examine the financial statements of Samson Corporation for the year 2014. The bookkeeper who maintains the financial records has prepared all the unaudited financial...

Q:

What are the alternative means to cope with the identified risk exposures? What are the costs and effectiveness of these alternative methods in treating risk? What are the advantages and...

Q:

Explain the assumptions that must be satisfied when a Poisson distribution adequately describes a random variable x.

Q:

Suppose that an automobile parts wholesaler claims that .5 percent of the car batteries in a shipment are defective. A random sample of 200 batteries is taken, and four are found to be defective. (1)...

Q:

In a murder trial in Los Angeles, a shoe expert stated that the range of heights of men with a size 12 shoe is 71 inches to 76 inches. Suppose the heights of all men wearing size 12 shoes are...

Q:

Use the currency exchange rates in Table 3.2 to calculate the equivalent amounts of currencies.

Q:

If Currency R strengthens relative to Currency S, will the exchange rate in terms of units of S per unit of R increase or decrease? Explain.

Q:

If the number of US$ per C$1.00 declines from 0.94168 to 0.92679, what will be the change in the C$ price per ounce of gold which a Canadian gold mine sells at the international price of US$975 per...