Homework Help is Here – Start Your Trial Now!
Math
Statistics
Two independent random variables, X1 and X2, follow Negative Binomial distributions with parameters (p, k1) and (p, k2), respectively. Show that their sum X1+X2 follows a Negative Binomial distribution with parameters p and (k1+k2).

Two independent random variables, X1 and X2, follow Negative Binomial distributions with parameters (p, k1) and (p, k2), respectively. Show that their sum X1+X2 follows a Negative Binomial distribution with parameters p and (k1+k2).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
M3
Two independent random variables, X1 and X2, follow Negative Binomial distributions with parameters (p, k1) and (p, k2), respectively. Show that their sum X1+X2 follows a Negative Binomial distribution with parameters p and (k1+k2). The daily number of claims for a household insurance portfolio has a Negative Binomial distribution with p=0.3 and k=2.5. Assuming that the claim numbers are independent from one day to the other for this portfolio, calculate the following quantities. (i) Probability of 6 claims in four days. (ii) Expected number of claims in a six day period. (iii) Given that there were 4 claims in the first 3 days, the probability of 3 more claims in the next two days.
Transcribed Image Text:Two independent random variables, X1 and X2, follow Negative Binomial distributions with parameters (p, k1) and (p, k2), respectively. Show that their sum X1+X2 follows a Negative Binomial distribution with parameters p and (k1+k2). The daily number of claims for a household insurance portfolio has a Negative Binomial distribution with p=0.3 and k=2.5. Assuming that the claim numbers are independent from one day to the other for this portfolio, calculate the following quantities. (i) Probability of 6 claims in four days. (ii) Expected number of claims in a six day period. (iii) Given that there were 4 claims in the first 3 days, the probability of 3 more claims in the next two days.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS