A random variable X follows a Poisson distribution, X~Pois (2), with parameter 1. a) Prove that the characteristic function (CF) of the random variable X is Ø, (t) = e²(e¹-1). b) Use the CF in (a) to find the mean and variance of the random variable X.
A random variable X follows a Poisson distribution, X~Pois (2), with parameter 1. a) Prove that the characteristic function (CF) of the random variable X is Ø, (t) = e²(e¹-1). b) Use the CF in (a) to find the mean and variance of the random variable X.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![QUESTION 4
A random variable X follows a Poisson distribution, X~Pois (2), with parameter 1.
a)
Prove that the characteristic function (CF) of the random variable X is Ø₂(t) = e²(eit-1).
b)
Use the CF in (a) to find the mean and variance of the random variable X.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7f442cf-541d-4442-b6c8-0606c8499d0b%2Fbece75d7-a93a-446d-9624-613c5c50fedc%2Fc9f6m2c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:QUESTION 4
A random variable X follows a Poisson distribution, X~Pois (2), with parameter 1.
a)
Prove that the characteristic function (CF) of the random variable X is Ø₂(t) = e²(eit-1).
b)
Use the CF in (a) to find the mean and variance of the random variable X.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Similar questions
- Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman