ABSTRACT
This chapter describes populations and samples from a population using the language of probability. Many populations are well described by the normal distribution; others are not. For example, a population may be multimodal, not symmetric, or have longer tails than the normal distribution. Many other families of distributions have been defined to describe different populations. The uniform distribution on [a, b] is useful to describe populations that have no preferred values over their range. For a finite range of values, the sample function can choose one with equal probabilities. The uniform distribution would be used when there is a range of values that is continuous. The exponential distribution is an example of a skewed distribution. It is a popular model for populations such as the length of time a light bulb lasts. The lognormal distribution is a heavily skewed continuous distribution on the positive numbers.
