Engineering Biostatistics

Chapter 5 Random Variables

The generation of random numbers is too important to be left to chance.

– Robert R. Coveyou

WHAT IS COVERED IN THIS CHAPTER

 

• Definition of Random Variables and Their Basic Characteristics
• Discrete Random Variables: Bernoulli, Binomial, Poisson, Hypergeometric, Geometric, Negative Binomial, and Multinomial
• Continuous Random Variables: Uniform, Exponential, Gamma, Inverse Gamma, Beta, Double Exponential, Logistic, Weibull, Pareto, and Dirichlet
• Transformation of Random Variables
• Markov Chains

5.1 Introduction

Thus far we have been concerned with random experiments, events, and their probabilities. In this chapter we will discuss random variables and their probability distributions. The outcomes of an experiment can be associated with numerical values, and this association will help us arrive at the definition of a random variable.

A random variable is a variable whose numerical value is determined by the outcome of a random experiment.

Thus, a random variable is a mapping from the sample space of an experiment, S, to a set of real numbers. In this respect, the term random variable is a misnomer. The more appropriate term would be random function or random mapping, given that X maps a sample space S to real numbers. We generally denote random variables by capital letters X,Y,Z,….

Example 5.1. Three Coin Tosses. Suppose a fair coin is ...