Homework Help is Here – Start Your Trial Now!
Math
Statistics
2.15. a) Prove that if YE(A), then for all t and s, P{Y>t+sY>t} = P{Y > s}. (2.16) b) Prove that if Y is absolutely continuous, positive and satisfies (2.16), then Y has an exponential distribution. [Hint: Prove that the survivor function Sy(t) = P{Y> t} fulfills the func- tional equation Sy(t + 8) = Sy(t) Sy(s) for s,t> 0.]

2.15. a) Prove that if YE(A), then for all t and s, P{Y>t+sY>t} = P{Y > s}. (2.16) b) Prove that if Y is absolutely continuous, positive and satisfies (2.16), then Y has an exponential distribution. [Hint: Prove that the survivor function Sy(t) = P{Y> t} fulfills the func- tional equation Sy(t + 8) = Sy(t) Sy(s) for s,t> 0.]

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
2.15. a) Prove that if Yª E(X), then for all t and s, P{Y >t+s]Y > t} = P{Y > s}. (2.16) b) Prove that if Y is absolutely continuous, positive and satisfies (2.16), then Y has an exponential distribution. [Hint: Prove that the survivor function Sy(t) = P{Y > t} fulfills the func- tional equation Sy(t+s) = Sy(t) Sy(s) for s, t > 0.]
Transcribed Image Text:2.15. a) Prove that if Yª E(X), then for all t and s, P{Y >t+s]Y > t} = P{Y > s}. (2.16) b) Prove that if Y is absolutely continuous, positive and satisfies (2.16), then Y has an exponential distribution. [Hint: Prove that the survivor function Sy(t) = P{Y > t} fulfills the func- tional equation Sy(t+s) = Sy(t) Sy(s) for s, t > 0.]
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

Please solve letter b.

2.15. a) Prove that if Yª E(X), then for all t and s, P{Y >t+s]Y > t} = P{Y > s}. (2.16) b) Prove that if Y is absolutely continuous, positive and satisfies (2.16), then Y has an exponential distribution. [Hint: Prove that the survivor function Sy(t) = P{Y > t} fulfills the func- tional equation Sy(t+s) = Sy(t) Sy(s) for s, t > 0.]
Transcribed Image Text:2.15. a) Prove that if Yª E(X), then for all t and s, P{Y >t+s]Y > t} = P{Y > s}. (2.16) b) Prove that if Y is absolutely continuous, positive and satisfies (2.16), then Y has an exponential distribution. [Hint: Prove that the survivor function Sy(t) = P{Y > t} fulfills the func- tional equation Sy(t+s) = Sy(t) Sy(s) for s, t > 0.]
Solution
Bartleby Expert
SEE SOLUTION
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