# Probability Distributions Worksheets

A35
A P P E N D I X C . 5
Probability Distributions
C.5 Probability Distributions
Construct frequency distributions.
Find probability distributions.
Frequency Distributions
As discussed in Section 11.1, a function that assigns a numerical value to each of
the outcomes in a sample space is called a random variable. For instance, if an
experiment consists of tossing three coins, then the outcomes could be assigned
the numbers 3, 2, 1, and 0, depending on the number of heads in the outcome.
Definition of Discrete Random Variable
Let be a sample space. A random variable is a function that assigns a
S
x
numerical value to each outcome in
S.
If the set of values taken on by the
random variable is finite, then the random variable is discrete.
The number of times a specific value of
x
occurs is the frequency of
x
and
is denoted by
n x .
A table showing the frequency of all possible values of the
random variable is called a frequency distribution.
Example 1
Finding Frequencies
Three people are asked whether they enjoy watching horror movies. A random
S T U D Y T I P
variable assigns the number 0, 1, 2, or 3 to each possible outcome, depending on
In Example 1, note that the
the number of “yes” responses.
sample space consists of eight
S
YYY, YYN, YNY, YNN, NYY, NYN, NNY, NNN
outcomes, each of which is
equally likely. The sample space
does not consist of the outcomes
3
2
2
1
2
1
1
0
“zero yes responses,” “one yes
Find the frequencies of 0, 1, 2, and 3.
response,”, “two yes responses,”
To find the frequencies, simply count the number of occurrences of
SOLUTION
and “three yes responses.” You
each value of the random variable, as shown in the frequency distribution below.
cannot consider these events to
be outcomes because they are
not equally likely.
Random variable, x
0
1
2
3
1
3
3
1
Frequency of x, n x
CHECKPOINT 1
You have pennies, nickels, and dimes in your pocket. You remove one coin from
your pocket at random, then another. A random variable assigns the number 0,
1, or 2 to each possible outcome, depending on the number of pennies that you
remove. Find the frequencies of 0, 1, and 2.