Discrete Probability Distributions

Previously, we looked at probability in terms of a probability experiment, the outcomes of the experiment, and the associated probabilities of the outcomes of those experiments.  These ideas can be extended to the idea of random variables and probability distributions.  Random variables and their associated probability distributions allow us to study populations of data and answer probability questions about those populations.

For example, suppose a student takes a ten-question, true-false quiz. Because the student had such a busy schedule, they could not study and guesses randomly at each answer.  What is the probability of the student passing the test with at least [latex]70\%[/latex] ([latex]7[/latex] out of [latex]10[/latex] correct answer)?  In this case, the random variable we are interested in is the number of correct answers the student got on the test, and we want to find the probability the student got [latex]7[/latex] or more correct answers on the quiz.

As another example, suppose a company is interested in the number of long-distance phone calls their employees make during the peak time of the day.  Suppose the average is [latex]20[/latex] calls.  What is the probability that the employees make more than [latex]20[/latex] long-distance phone calls during the peak time?  Here, the random variable we are interested in is the number of long-distance phone calls made during the peak time and we want to find the probability the number of long-distance phone calls is greater than [latex]20[/latex].

As seen in the above examples, a random variable describes the outcomes of a statistical experiment in words.  The values a random variable takes on are numbers associated with the outcomes of the experiment.  These two examples illustrate two different types of probability problems involving discrete random variables.  Recall that discrete data are data that can be counted.  In this chapter, we want to define random variables, construct the probability distribution for an associated random variable, and use the probability distribution to calculate probabilities for the random variable.

“4.1 Introduction to Discrete Random Variables” from Introduction to Statistics by Valerie Watts is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.