Exercise 41 (i) On average, Amy receives 10 text messages per hour. Suppose the arrival times of the text mes- sages 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 7am in the 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 7.04am 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 7.10am?

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