Probably Not, 2nd Edition

2Probability Distribution Functionsand Some Math Basics

The Probability Distribution Function

(Aside) This section includes a primer/review of the mathematical notations introduced in this chapter. The mathematics is mostly just combinations of adding, subtracting, multiplying, and dividing lists of numbers. Since – in many cases – we will be dealing with very many numbers at a time (hundreds or even thousands of them), it is impractical to write out all of the numbers involved in a given calculation. What we do instead is introduce a summarizing notation that includes things such as subscripted variables, summation signs.

The probability distribution function (PDF) is a powerful tool for studying and understanding probabilities. However, before discussing it is important to introduce the idea of a mathematical function. A mathematical function, or more simply, a function, is the mathematical equivalent of a food processor: you pour in one or more numbers, push the “grind” button for a few seconds, and pour out the resulting concoction.¹ Three important facts were just presented:

1. One or more numbers, usually called variables or independent variables go into the function, depending upon the particular function “recipe” we're dealing with.
2. The function somehow processes these numbers to produce a result (a number) which is usually called the value of the function for the particular variable(s) that went into the function.
3. The function produces exactly one value (result) for ...