A Statistical Problem on Laptop Uptimes

Suppose you are in a large university campus. Most students here use laptops, and if you look around, you’d see most of them either working, listening to music or doing something else on their laptops. Suppose now you think of a quick project, of listing the uptimes of the laptops (how long they’ve been running). In Windows this is quite simple. Under the ‘Performance’ tab in Task Manager, you’ll notice that ‘Uptime’ gives the duration for which the laptop has been running. This timer, however, keeps counting from where it left off if you resume from hibernation, as it should, but we shall assume that no such cases happen in our campus.

Now, the campus is huge, and many students are using their laptops. You figure out some methodical way of visiting each student so that there are no over- or under-counting errors. But it takes you quite a while to visit all of them and note down their uptimes. So that if, for example, it took you six hours to collect all the data, then you took the last uptime reading six hours after the first.

If we assume a very large campus where the uptimes of the laptops of different students are completely independent of each other, the questions are the following:

1. On an average, is it going to make any difference to the statistics you collected, if instead of taking a long time to go around the campus, you could somehow acquire all of the uptimes at one instant of time?

2. Is the data you collected going to be distributed differently from that of the maximum uptimes of student laptops (duration before they shut it down)?

Unless I find myself without the time and effort, I plan to return and solve it in this blog post. (I haven’t solved it yet.)

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2 thoughts on “A Statistical Problem on Laptop Uptimes

  1. yes, it looks to me it would.for the distributions to be comparable, more than some hundreds of students would be required. and then it would depend on the time when you were collecting data at one instant.

    • You’re right about both the things. However, when I thought of this problem, I was thinking in idealized terms like a population of computers which all get turned on and off according to the same distribution all the time, so that the time of the instantaneous data collection wouldn’t matter. Also, I was interested in the statistics of a large population that you can theoretically work out.
      Yeah, physics people tend to oversimplify. But I have a solution in the simplified case which I plan to post here when I’m finished.
      Thanks for dropping by!

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