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A Waiting-Time Surprise

by Richard Parris

This article originally appeared in:
College Mathematics Journal
January, 2008

Subject classification(s): Statistics and Probability | Probability | Univariate Distributions
Applicable Course(s): 6.1 Probability & Statistics | 7.2 Probability

Consider the sum of \(n\) random real numbers, uniformly distributed in the unit interval. Although the expected value of this sum is \(n/2\), the value of \(n\) for which this sum first exceeds a given target value \(t\) is expected to be more than \(2t\), by an amount that is asymptotically constant.

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Capsule Course Topic(s):
Probability | Continuous Distributions, Other
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