1. I am waiting for two friends to arrive at my house. The time until A arrives is exponentially distributed with rate λs, and the time until B arrives is exponentially distributed with rate λb. Once they arrive, both will spend exponentially distributed times, with respective rates μa and μb at my home before departing. The four exponential random variables are independent. (a) What is the probability that A arrives before and departs after B? (b) What is the expected time of the last departure?
1. I am waiting for two friends to arrive at my house. The time until A arrives is exponentially distributed with rate λs, and the time until B arrives is exponentially distributed with rate λb. Once they arrive, both will spend exponentially distributed times, with respective rates μa and μb at my home before departing. The four exponential random variables are independent. (a) What is the probability that A arrives before and departs after B? (b) What is the expected time of the last departure?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 22E
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1. I am waiting for two friends to arrive at my house. The time until A arrives is exponentially distributed with rate λs, and the time until B arrives is exponentially distributed with rate λb. Once they arrive, both will spend exponentially distributed times, with respective rates μa and μb at my home before departing. The four exponential random variables are independent.
(a) What is the probability that A arrives before and departs after B?
(b) What is the expected time of the last departure?
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