Continuous Random Variables

Abstract

In Chapter 2, we discussed discrete random variables. These random variables took on finite or countably many values. Here we will study random variables whose set of possible values is uncountable. For example, the price of a stock with its erratic ups and downs can be modeled as a random variable, and since in principle the price can be any positive number, modeling it using a continuous random variable is a sensible strategy. Another example is the waiting time for the first customer to enter a store, if you like, your neighborhood Starbucks. The waiting time can be any positive number (if we could measure it with sufficient precision), so a continuous random variable could be a good model.