Introduction to Chapter 4: Discrete Random Variables
Figure 4.1. You can use probability and discrete random variables to calculate the likelihood of lightning striking the ground five times during a half-hour thunderstorm. (Credit: Leszek Leszczynski)
Let us begin with two different examples of the types of probability problems we’ll be able to model using the techniques of this chapter.
Example 1: Suppose a student takes a ten-question, true-false quiz. Because the student had such a busy schedule, they could not study and guess randomly at each answer. What is the probability of the student passing the quiz with at least a 70%?
Example 2: Small companies might be interested in the number of unread emails sitting in their employee’s mailboxes. If the average number of unread emails is 100 at the end of the workday, what is the probability that on a given day, the employees have more than 120 unread emails at the end of the workday?
Each of these probabilities can be found if we know the distribution of the corresponding discrete random variable. Recall that discrete data are data that you can count. A random variable describes the outcomes of a statistical experiment in words. The values of a random variable can vary with each repetition of an experiment.
Collaborative Exercises
Section 4.1
Collaborative Exercise
Toss a coin ten times and record the number of heads. After all members of the class have completed the experiment (tossed a coin ten times and counted the number of heads), fill in Table 1. Let X = the number of heads in ten tosses of the coin.
x
Frequency of x
Relative Frequency of x
Table 1
Which value(s) of x occurred most frequently?
If you tossed the coin 1,000 times, what values could x take on? Which value(s) of x do you think would occur most frequently?
