# A Waiting-Time Surprise

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.

Author(s):
Richard Parris
Publication Date:
Monday, June 9, 2014
Original Publication Source:
College Mathematics Journal
Original Publication Date:
January, 2008
Subject(s):
Statistics and Probability
Probability
Univariate Distributions
Topic(s):
Probability
Continuous Distributions, Other
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Applicable Course(s):
6.1 Probability & Statistics
7.2 Probability
Modify Date:
Monday, June 9, 2014