Let X exp(A) be an exponential random variable. (a) Compute P(X > t) for some positive real number t. (b) Compute P(X > t + s|X > s) for some positive real numbers t and s. (c) If for a random variable X, P(X > t) = P(X > t + s|X > s), we call it memoryless. Justify this name. Is exponential distribution a memoryless random variable?
Let X exp(A) be an exponential random variable. (a) Compute P(X > t) for some positive real number t. (b) Compute P(X > t + s|X > s) for some positive real numbers t and s. (c) If for a random variable X, P(X > t) = P(X > t + s|X > s), we call it memoryless. Justify this name. Is exponential distribution a memoryless random variable?
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
Transcribed Image Text:Let X~ exp(X) be an exponential random variable.
(a) Compute P(X > t) for some positive real number t.
(b) Compute P(X > t+s|X > s) for some positive real numbers t and s.
(c) If for a random variable X, P(X > t) = P(X > t + s|X > s), we call it memoryless. Justify this name. Is
exponential distribution a memoryless random variable?
Transcribed Image Text:Let X~ exp(X) be an exponential random variable.
(a) Compute P(X > t) for some positive real number t.
(b) Compute P(X > t+s|X > s) for some positive real numbers t and s.
(c) If for a random variable X, P(X > t) = P(X > t + s|X > s), we call it memoryless. Justify this name. Is
exponential distribution a memoryless random variable?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
Similar questions
- Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics 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 Learning
Elementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman