Introduction

In chapter 3 we considered the normal distribution largely due to its similarity to the distribution of data observed in many experiments involving repeat measurements of a quantity. In particular, the normal distribution is useful for describing the spread of values when continuous quantities such as temperature or time interval are measured.

Another important category of experiment involves counting. As examples, we may count the number of electrons scattered by a gas, the number of charge carriers thermally generated in an electronic device, or the number of beta particles emitted by a radioactive source. In these situations, distributions that describe discrete quantities must be considered. In this chapter we consider two such distributions important in science: the binomial and Poisson distributions.

The binomial distribution

One type of experiment involving discrete variables entails removing an object from a population and classifying that object in one of a finite number of ways. For example, we might test an electrical component and classify it ‘within specification’ or ‘outside specification’. Owing to the underlying (and possibly unknown) processes causing components to fail to meet the specification, we can only give a probability that any particular component tested will satisfy the specification. When n objects are removed from a population and tested, or when a coin is tossed n times, we speak of performing n trials. The result of a test (e.g. ‘pass’) or the result of a coin toss (e.g. ‘head’) is referred to as an outcome.