Question: Prove Theorem 5.6 by first determining E(X) and E[X(X + 1)]. Theorem 5.6 The mean and the variance of the negative binomial distribution are

Prove Theorem 5.6 by first determining E(X) and E[X(X + 1)].
Theorem 5.6
The mean and the variance of the negative binomial are
µ = k/θ and σ2 = k/θ(1/θ – 1)

Step by Step Solution

★★★★★

3.18 Rating (192 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

y x 2 m k 1 y x 2 ... 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)

583-S-J-P-D (781).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Prove Theorem 5.5. Theorem 5.5 b*(x;k,) = k/x. b(k;x,)

Prove that the p.f. of the negative binomial distribution can be written in the following alternative form: f(xir,p) =|C)pr(-11- pD for x 0, 1. 2. otherwise.

Prove Theorem 5.3. Theorem 5.3 If X has a binomial distribution with the parameters n and and Y = X/n , then E(Y) = and 2Y = (1 )/n

Q1. BIG Corporation produces just about everything but is currently interested in the lifetimes of its batteries. To investigate its new line of Ultra batteries, BIG randomly selects 1000 Ultra...

Downloaded 02/28/15 to 132.174.255.3. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php 15.7. Exercises 475 changes and we laugh no more. While...

Add more details to explain why and how to fix it. Thank you so much. 5. Write a detailed description of the error(s) in these class definitions. Do not fix the code. public class Test Class {...

BA 1605: Midterm Recap (Due: Feb. 27, 2015) Name _____________________________ 50 Student ID _____________________________ Section 01B 10:00~11:20 am Section 02B 01:00~02:20 pm [Questions 4 ~ 7] The...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

1 2.3 Definition of a Discrete Probability Function Definition: Let S be a discrete sample space from some experiment. A function P, defined on all events in S, is said to be a probability function...

Please explain to me clearly and show how to do the two suppositions in the (question) file. Please take a look at the (notes) file and see the material up to the questions will be needed to answer...

(10 points) Part I: Sally needs to choose between 2 health insurance plans. Assume Sally will use $4,500 worth of medical services this year. Is she better off choosing plan A or plan B? Briefly show...

Describe an effective process for performance appraisals. Explain why it is the best process to use.

In the following examples, is inflation creating winners and losers at no net cost to the economy or is it imposing a net cost on the economy? Explain. If inflation is imposing a net cost on the...

An orderly-working monetary union implies: a) a common currency for its member countries national central banks; b) fiscal and monetary policy coordination; c) fiscal transfers between its member...

How many permutations of three items can be selected from a group of six? Use the letters A, B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F.

Consider the experiment of tossing a coin three times. a. Develop a tree diagram for the experiment. b. List the experimental outcomes. c. What is the probability for each experimental outcome?

The amount of sodium (in milligrams) in one serving for a random sample of three different foods is listed in the table below. At the 0.10 level of significance, is there sufficient evidence to...

0.8 Let S=$100,K=$95,=30%,r=8%,T=1, and =0. Let u=1.3,d=0.8, and n=2. Construct the binomial tree for a European put option. At each node provide the premium, , and B. 0.8 Let...

Suzy Q is the CEO of a financial services firm. What action should Suzy take to be sure the fitm avoids moral hazards? Suzy must increase hiring and develop influential relationships with government...