Graduation Year


Date of Submission


Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Arts



Reader 1

Mark Huber

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Approximation algorithms employing Monte Carlo methods, across application domains, often require as a subroutine the estimation of the mean of a random variable with support on [0,1]. One wishes to estimate this mean to within a user-specified error, using as few samples from the simulated distribution as possible. In the case that the mean being estimated is small, one is then interested in controlling the relative error of the estimate. We introduce a new (epsilon, delta) relative error approximation scheme for [0,1] random variables and provide a comparison of this algorithm's performance to that of an existing approximation scheme, both establishing theoretical bounds on the expected number of samples required by the two algorithms and empirically comparing the samples used when the algorithms are employed for a particular application.


  • Best Senior Thesis in Mathematics