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Browse Classroom Capsules and Notes

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Displaying 11 - 20 of 70

Bernstein's Examples on Independent Events

When the sample space is too small, then Bernstein's examples on independent events fail.

Tennis (and Volleyball) without Geometric Series

Solving an expected value problem without using geometric series

Tennis with Markov

In the game of tennis, if the probability that player \(A\) wins a point against player \(B\) is a constant value \(p\), then the probability that \(A\) will win a game from deuce is \(p^2/(1 - 2p...

Why is the Sum of Independent Normal Random Variables Normal?

The authors give two proofs, one geometric and one algebraic, to provide insight into why the sum of independent normal. random variables must be normal.

Shanille Practices More

A solution to a probabilistic Putnam Exam Problem is presented.

Coin Flipping, Dynamical Systems, and the Fibonacci Numbers

This article links two seemingly unrelated problems, one in probability and the other in dynamical systems, and shows they are actually one involving Fibonacci numbers.

The Importance of a Game

Probabilistic analysis of the importance of a game in a series of games in a competition

The Birthday Problem Revisited
The author derives approximations for the probability arising in birthday-type problems without using calculus.
A Papal Conclave: Testing the Plausibility of a Historical Account

The author applies basic probability theory to the papal election of 1458.

An Application of the Dominated Convergence Theorem to Mathematical Statistics
The authors give a "simple, conceptual" proof of the fact that the t-distribution converges to the standard normal. The proof is accessible to undergraduates.

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