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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?

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?

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
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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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