41. (i) On average, Amy receives 10 text messages per hour. Suppose the arrival times of the text messages are independent and exponentially distributed. What is the probability that Amy has to wait more than 8 minutes for the next text message? (ii) Amy woke up at 7 am in morning. She is eagerly waiting for a text message from her new boyfriend. On a usual day, she waits only about 5 minutes for his first message of the day after waking up, but the actual wait time is exponentially distributed. Now it is 7.04 am and there is no message yet... How much longer do you expect her to wait for his message? What is the probability that his message will be received after 7.10 am?

41. (i) On average, Amy receives 10 text messages per hour. Suppose the arrival times of the text messages are independent and exponentially distributed. What is the probability that Amy has to wait more than 8 minutes for the next text message? (ii) Amy woke up at 7 am in morning. She is eagerly waiting for a text message from her new boyfriend. On a usual day, she waits only about 5 minutes for his first message of the day after waking up, but the actual wait time is exponentially distributed. Now it is 7.04 am and there is no message yet... How much longer do you expect her to wait for his message? What is the probability that his message will be received after 7.10 am?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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