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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
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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.]
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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.]
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