Question: Show that if X has a negative binomial distribution NBIN(r,p), then E[(r 1)/(r + X 1)] = p.

Show that if X has a negative binomial distribution NBIN(r,p), then E[(r − 1)/(r + X − 1)] = p.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock 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 Nonparametric Statistical Inference Questions!

Q:

The following distributions arise on the basis of assumptions similar to those leading to (1.1)(1.3). (i) Independent trials with constant probability p of success are carried out until a preassigned...

Q:

5.23 A random variable X has the negative binomial distribution, pr(X = k) = n + k 1 n 1 p q k 1 p q n , for k 0, in which q = 1+ p. Show that the expectation and variance of X are given by...

Q:

BE562: Problem Set 3 Fall 2016 Due 10/21/2016 8PM 1. Hidden Markov Models and Protein Structure (20 pts) One biological application of hidden Markov models is to determine the secondary structure...

Q:

3. Suppose X has a negative binomial distribution with parameters r and p, and Y has a negative binomial distribution with parameters s and p. Show that X +Y has a negative binomial distribution with...

Q:

16. Let X have the negative binomial distribution with parameters r and p. Thus, X counts the total number of Bernoulli trials until the rth success. Next, let X1 denote the number of trials up to...

Q:

Let R Geom(p). Conditional on R = r, suppose X has a negative binomial distribution with parameters r and p. Show that the marginal distribution of X is geometric. What is the parameter?

Q:

Let X have the negative binomial distribution with parameters r and p. Assume that r is known. Show that the Fisher information in X is I (p) = r/[p2(1 p)].

Q:

7.38 Let X have the negative binomial distribution f (x) = x 1 r 1 pr (1 p) xr for x = r,r + 1,... (a) Obtain the maximum likelihood estimator of p. (b) For one engineering application, it is...

Q:

The following distributions arise on the basis of assumptions similar to those leading to (1.1)(1.3). (i) Independent trials with constant probability p of success are carried out until a preassigned...

Q:

6. (Fisher information) Recall the definition of a negative binomial variable X with parameters p and m introduced in Problem 3 of Homework 1. Compute the Fisher information I(p) contained in X about...

Q:

A $1000 par bond has a coupon rate of 7% and pays its fixed income payment twice annually. This bond has 14.0 years remaining until maturity. The current market rate (i.e., internal rate of return,...

Q:

You purchased 1,000 shares of Koogal five years ago at $30 per share. Today Koogal is repurchasing its shares through a fixed-price tender offer price of $80 per share. What is the amount of...

Q:

Which of the following statements is accurate? Group of answer choices If equipment is expected to be sold for more than its book value at the end of a project's life, this will result in a profit....

Q:

What do you think is your strongest component of cultural intelligence? Your weakest? How would you go about shoring up your weaknesses?