Introduction

In chapter 3 we considered the normal distribution largely due to its similarityto the distribution of data observed in many experiments involving repeatmeasurements of a quantity. In particular, the normal distribution is useful fordescribing the spread of values when continuous quantities such as temperatureor time interval are measured.

Another important category of experiment involves counting. As examples, we maycount the number of electrons scattered by a gas, the number of charge carriersthermally generated in an electronic device, or the number of beta particlesemitted by a radioactive source. In these situations, distributions thatdescribe discrete quantities must be considered. In this chapter we consider twosuch distributions important in science: the binomial and Poissondistributions.

The binomial distribution

One type of experiment involving discrete variables entails removing an objectfrom 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 tofail to meet the specification, we can only give a probability that anyparticular component tested will satisfy the specification. Whenn objects are removed from a population and tested, or whena coin is tossed n times, we speak of performingn trials. The result of a test (e.g. ‘pass’)or the result of a coin toss (e.g. ‘head’) is referred to as anoutcome.