Contemporary Mathematics

# Projects

### Projects

1. The Binomial Distribution is one of many examples of a discrete probability distribution. Other examples include the Geometric, Hypergeometric, Multinomial, Poisson, and Negative Binomial Distributions. Choose one of these distributions, and find out what makes it different from the Binomial Distribution. In what situations can it be applied? How is it used? Once you have an idea of how it’s used, write a series of five questions like the ones in this chapter that can be answered with that distribution, and find the answers.
2. Binomial is a word that also comes up in algebra; the word describes polynomials with two terms. At first glance, there isn’t much to indicate that these two uses of the word are related, but it turns out there is a connection. Explore the connection between the Binomial Distribution and the algebraic concept of binomial expansion, (the process of multiplying out expressions like $(x+y)n(x+y)n$ for a positive whole number $nn$). Search for a connection with the mathematical object known as Pascal’s Triangle.
3. Hazard is a dice game that was mentioned in Chaucer’s Canterbury Tales. It was a popular game of chance played in taverns and coffee houses well into the 18th century; its popularity at the time of the foundation of probability theory means that it was a common example in early texts on finding expected values and probabilities. Find the rules of the game, and get some practice playing it. Then, analyze the choices that the caster gets to make, and decide which is most advantageous, using the language of expected values.