There is really no shortcut to taking a full introductory course to cover the basic concepts. In this section we cover the most important ideas that the reader should be familiar with. Think of this as a brief refresher to old ideas rather than the true exposure to new topics.

Historically, the development of probability predates the use of statistics by several centuries. The need for probability came about in studies of games of chance. Gamblers were then, as they are today, seeking an edge in an easy way to make a fortune. Of course, if there was a way to do so, there would be many wealthy mathematicians today. Instead, mathematicians have shown that there is no winning strategy. Card-counting at blackjack requires considerable practice and great concentration, and only then does it provide a slight edge to the player.

Statistics, on the other hand, was very much a product of the industrial revolution. Large numbers of items needed to be produced in a uniform fashion, and random variability stood in the way. Statistics became a scientific discipline in the early 1900s with the development of two important innovations: the chi-squared test, due to K. Pearson, and Student's t-test. Both of these topics are reviewed later in this chapter.

Binomial Distribution

The binomial distribution is one of the basic mathematical models for describing the behavior of a random outcome.