Question: Let Y be a negative binomial random variable with parameters r and p. Then it can be shown that W = Y - r is

Let Y be a negative binomial random variable with parameters r and p. Then it can be shown that W = Y - r is also a negative binomial random variable, where W represents the number of failures before the rth success is observed. Use the facts that

E(Y) rq and o to show that E(W) rq and o

Step by Step Solution

★★★★★

3.45 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

A negative binomial random variable is the number X of repe... 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

Students Have Also Explored These Related Statistics For Engineering And The Sciences Questions!

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

Let X be a binomial random variable with parameters (n, p). What value of p maximizes P{X = k}, k = 0, 1, . . . , n? This is an example of a statistical method used to estimate p when a binomial (n,...

Let W be a gamma random variable with parameters (t, Î²), and suppose that conditional on W = w, X1, X2, . . . ,Xn are independent exponential random variables with rate w. Show that the...

can you please help me with mathematical Statistics 1. /12 marks) Let X be a binomially distributed random variable with parameters n and p. i. (12 marks) Show that Var(X) = np(1 - p). (See hint on...

Problem 29.* Let A and B be events with P(A) > 0 and P(B) > 0. We say that an event B suggests an event A if P(A| B) > P(A), and does not suggest event A if P(A| B) 0. Show that B suggests A if and...

Let X be a binomial random variable with parameters we and p. Here is another way to prove that 1 1 2 n Pr[X is odd] = 5 (+33). LetX=X1+-~Xn where Pr[Xi=1]=pandPr[X,-=0]=1p. For each i, let Y} be a...

Could you help me to solve part a and b? As for part a I got E(X^2)=n^2*p^2 and part b) E(W)=4*n*p+6*m*pi, Var(W)=16(np(1-p)+36(mpi(1-pi). Could you write what the correct answers are? Thank you! 1....

Discussion Questions 1 Let X,, X, and X, be independent, identically distributed random variables with mean u and variance of, and A = (X, + X, + X;)/3. Is A an unbiased estimator of ! 2 Suppose that...

5.39 Let Y denote a negative binomial random variable with p 0.4. Find P(Y 4) if a r 2 b r 4

If X is a Negative Binomial random variable with parameters p and r, then find the moment generating function of X. In Exercise 1 P(X = x) = px(x) = (1- p)x-lp For x = 1, 2, 3,..., and pX(x) = 0...

In the Global Youth Tobacco Survey, conducted jointly by the World Health Organization and the US Centers for Disease Control and Prevention (CDC), a random sample of children aged 13 15 in various...

Recall that a conflict of interest scenario was presented to a sample of 205 marketing researchers and that 111 of these researchers disapproved of the actions taken. a. Let p be the proportion of...

6.9 Compare and contrast different production processes.

2 How would you evaluate the contributions of Roger Whiteside, Julian Metcalfe and Fred DeLuca in developing the industry?

The article "Microwave Observations of Daily Antarctic Sea Ice Edge Expansion and Contribution Rates" (IEEE Geo sci. and Remote Sensing Letters, 2006: 54-58) states that "The distribution of the...

A consumer is trying to decide between two long-distance calling plans. The first one charges a flat rate of 10 per minute, whereas the second charges a flat rate of 99 for calls up to 20 minutes in...

Evaluate the following: a. (6) b. (5/2) c. F(4; 5) (the incomplete gamma function) and F(5; 4) d. P(X 5) when X has a standard gamma distribution with = 7. e. P(3

Player Pressure Aggression Defence Endurance Overall score Rafael Nadal 96 81 80 86 Novak Djokovic Roger Federer 87 94 89 67 Daniil Medvedev 85 81 94 80 Dominic Thiem 85 79 79 93 Stefanos Tsitsipas...

Essence of Skunk Fragrances, Ltd., sells 7,600 units of its perfume collection each year at a price per unit of $810. All sales are on credit with terms of 1.5/15, net 60. The discount is taken by 75...

The following gives information about the proportion of a sample that agree with a certain statement. Use StatKey or other technology to find a confidence interval at the given confidence level for...