# A Waiting-Time Surprise

by Richard Parris

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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