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\newcommand{\mathds}{\mathbb}</math></div> For examples such as those in Exercises [[exercise:8b408c8df0 |Exercise]] and [[exercise:B52419720c |Exercise]], it might seem that at least you should not have to wait on average ''more'' | \newcommand{\mathds}{\mathbb}</math></div> For examples such as those in Exercises [[exercise:8b408c8df0 |Exercise]] and [[exercise:B52419720c |Exercise]], it might seem that at least you should not have to wait on average ''more'' than 10 minutes if the average time between occurrences is 10 minutes. Alas, even this is not true. To see why, consider the following assumption about the times between occurrences. Assume that the time between occurrences is 3 minutes with probability .9 and 73 minutes with probability .1. Show by simulation that the average time between occurrences is 10 minutes, but that if you come upon this system at time 100, your average waiting time is more than 10 minutes. | ||
than 10 minutes if the average time between occurrences is 10 minutes. Alas, even this is not | |||
true. To see why, consider the following assumption | |||
about the times between occurrences. Assume that the time between occurrences is 3 | |||
minutes with probability .9 and 73 minutes with probability .1. Show by | |||
simulation that the average time between occurrences is 10 minutes, but that if you come upon this | |||
system at time 100, your average waiting time is more than 10 minutes. | |||
Latest revision as of 21:40, 12 June 2024
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For examples such as those in Exercises Exercise and Exercise, it might seem that at least you should not have to wait on average more than 10 minutes if the average time between occurrences is 10 minutes. Alas, even this is not true. To see why, consider the following assumption about the times between occurrences. Assume that the time between occurrences is 3 minutes with probability .9 and 73 minutes with probability .1. Show by simulation that the average time between occurrences is 10 minutes, but that if you come upon this system at time 100, your average waiting time is more than 10 minutes.