Discrete Random Variables and Probability Distributions

Suppose a city’s traffic engineering department monitors a certain intersection during a one-hour period in the middle of the day. Many characteristics might be of interest to the observers, including the number of vehicles that enter the intersection, the largest number of vehicles in the left turn lane during a signal cycle, the speed of the fastest vehicle going through the intersection, the average speed of all vehicles entering the intersection. The value of each one of the foregoing variable quantities is subject to uncertainty—we don’t know a priori how many vehicles will enter, what the maximum speed will be, etc. So each of these is referred to as a random variable—a variable quantity whose value is determined by what happens in a chance experiment. There are two fundamentally different types of random variables, discrete and continuous. In this chapter we examine the basic properties and introduce the most important examples of discrete random variables. Chapter 3 covers the same territory for continuous random variables.