Chapter 7 - Random Variables: Working with Uncertain Numbers

Abstract

This chapter provides an overview of random variables. A random variable is a specification or description of a numerical result from a random experiment. A particular value taken on by a random variable, observation. The pattern of probabilities for a random variable is called its probability distribution. Random variables are either discrete (if all possible outcomes are listed) or continuous (if any number in a range is possible). Some random variables are actually discrete, but they can be worked with as if they are continuous. For a discrete random variable, the probability distribution is a list of the possible values together with their probabilities of occurrence. A random variable, X, has a binomial distribution if it represents the number of occurrences of an event out of n trials, provided (1) for each of the n trials, the event always has the same probability π of happening and (2) the trials are independent of one another. The chapter describes concepts related to discrete random variables and finding the mean and standard deviation. It provides definition of binomial distribution and proportionand discusses finding the mean and standard deviation along with visualizing probabilities through an explanation of the area under the curve.