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3 Introduction to Discrete Random Variables
Chapter Outline
3.1 Discrete Random Variables
3.2 PROBABILITYDISTRIBUTION
3.3 BINOMIALDISTRIBUTIONS ANDPROBABILITY
3.4 MULTINOMIALDISTRIBUTIONS
3.5 THEORETICAL ANDEXPERIMENTALSPINNERS
3.6 THEORETICAL ANDEXPERIMENTALCOINTOSSES
Introduction
In this chapter, you will learn about discrete random variables. Discrete random variables can take on a finite number
of values in an interval, or as many values as there are positive integers. In other words, a discrete random variable
can take on an infinite number of values, but not all the values in an interval. When you find the probabilities of
these values, you are able to show the probability distribution. A probability distribution consists of all the values of
the random variable, along with the probability of the variable taking on each of these values. Each probability must
be between 0 and 1, and the probabilities must sum to 1.
You will also be introduced to the concept of a binomial distribution. This will be discussed in depth in the next
chapter, but in this chapter, you will use a binomial distribution when talking about the number of successful events
or the value of a random variable. A binomial distribution is only used when there are 2 possible outcomes. For
example, you will use the binomial distribution formula for coin tosses (heads or tails). Other examples include
yes/no responses, true or false questions, and voting Democrat or Republican. When the number of possible
outcomes goes beyond 2, you use a multinomial distribution. Rolling a die is a common example of a multinomial
distribution problem.
In addition, you will use factorials again for solving these problems. Factorials were introduced in Chapter 2 for
permutations and combinations, but they are also used in many other probability problems. Finally, you will use a
graphing calculator to show the difference between theoretical and experimental probability. The calculator is an
effective and efficient tool for illustrating the difference between these 2 probabilities, and also for determining the
experimental probability when the number of trials is large.