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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.

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