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B2. (a) Let X ~ Exp(A). Show that P(X > x + y | X > y) = P(X > x). (b) The result proved in part (a) is called the "memoryless property". Why do you think it's called that? (c) When you get to certain bus stop, the average amount of time you have to wait for a bus to arrive is 20 minutes. Specifically, the time until the next bus arrives is modelled as an exponential distribution with expectation 1/λ = 20 minutes. Suppose you have already been waiting at the bus stop for 15 minutes. What is the expected further amount of time you still have to wait for a bus to arrive?

B2. (a) Let X ~ Exp(A). Show that P(X > x + y | X > y) = P(X > x). (b) The result proved in part (a) is called the "memoryless property". Why do you think it's called that? (c) When you get to certain bus stop, the average amount of time you have to wait for a bus to arrive is 20 minutes. Specifically, the time until the next bus arrives is modelled as an exponential distribution with expectation 1/λ = 20 minutes. Suppose you have already been waiting at the bus stop for 15 minutes. What is the expected further amount of time you still have to wait for a bus to arrive?

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter11: Rational And Irrational Numbers
Section: Chapter Questions
Problem 23CLR
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B2. (a) Let X ~ Exp(A). Show that P(X > x + y | X > y) = P(X > x). (b) The result proved in part (a) is called the "memoryless property". Why do you think it's called that? (c) When you get to certain bus stop, the average amount of time you have to wait for a bus to arrive is 20 minutes. Specifically, the time until the next bus arrives is modelled as an exponential distribution with expectation 1/λ = 20 minutes. Suppose you have already been waiting at the bus stop for 15 minutes. What is the expected further amount of time you still have to wait for a bus to arrive?
Transcribed Image Text:B2. (a) Let X ~ Exp(A). Show that P(X > x + y | X > y) = P(X > x). (b) The result proved in part (a) is called the "memoryless property". Why do you think it's called that? (c) When you get to certain bus stop, the average amount of time you have to wait for a bus to arrive is 20 minutes. Specifically, the time until the next bus arrives is modelled as an exponential distribution with expectation 1/λ = 20 minutes. Suppose you have already been waiting at the bus stop for 15 minutes. What is the expected further amount of time you still have to wait for a bus to arrive?
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