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Chapter 8: Discrete Probability Distributions
Definition: Random Variable
A random variable assigns one and only one numerical value to each point in
the sample space for a random experiment.
Notes:
Random variables are usually denoted by uppercase letters near the
end of the alphabet, such as X, Y, and Z.
We will use the corresponding lowercase letters to represent the
values of the random variables, such as
x
,
y
, and
z
.
Types of Random Variables
In our studies, we will encounter two types of random variables. These two
types of random variables are classified as
discrete
and
continuous
random
variables.
First we will define what we mean by a discrete random variable.
Definition: Discrete Random Variable
A discrete random variable is one that can assume a countable number of
possible values.
Examples of discrete random variables include the number of days it rained
in your community during the month of March; the number of defective
items in a lot; the number of children in a family; the number of days a
student is absent from classes during a semester; etc. Note the values for
these variables will be discrete in nature. For example, if
X
is the number of
days a student is absent from a particular course during a semester then this
is an example of a discrete random variable. So, if the total number of class
meetings is 36, then the possible values for
X
are
x
= 0, 1, 2, 3, …, 36.
Figure 8-3
displays the discrete possibilities for the number of student
absences.