Browse Classroom Capsules and Notes

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Exhaustive Sampling and Related Binomial Identities

This project uses a sampling problem to compute certain probabilities. In the process, certain binomial identities are established.

The Birthday Problem Revisited

A variation of the birthday problem is being considered: what is the probabibility of \(2\) out of \(n\) people to have their birthday on a particular day? Furthermore, this capsule...

The Disadvantage of Too Much Success.

The authors consider three cointossing models in which “too much success” is defined by the occurrence of success runs of a certain length which causes play to stop. The objective...

Teaching Tip: Actuarial Science and Gompertz’s Law of Mortality

The author provides a simple context and some history in which actuarial computations take place.

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...

An Upper Bound for the Expected Difference between Order Statistics

The authors study the upper bound for the expected differences between order statistics of a distribution.

How Fast Will We Lose?

The probability of losing in exactly \(n\) steps of the gambler`s ruin game is investigated.

Winning at Rock-Paper-Scissors

Experiments show that people tend to behave "unfairly" in the fair R-P-S games. The authors find the optimal strategies for two cases.

Maybe the Price Doesn't Have to Be Right: Analysis of a Popular TV Game Show

The authors use a popular TV show to demonstrate probability theory.

Cars, Goats, \(\pi\) and \(e\)

The author proposes two extensions of the Monte Hall problem, with solutions involving the numbers \(\pi\) and \(e\), respectively.