Unit 5
Section 4.1
4.1: Probability Distributions

Variables – a characteristic or attribute that can
assume different variables.

Within this unit, since we are discussing probability,
the variables are called random variables.

Random Variable – is a variable whose values are
determined by chance.

Variables can also be discrete (have a finite
number of values or an infinite number of
countable values) or continuous (can assume all
values between any two given intervals.
Section 4.1
 Discrete
Probability Distribution – lists each
possible value the random variable can
assume, together with its probability.
 The
probabilities are determined theoretically
or by observation.
 The probability of each value must be
between 0 and 1.
 The sum of all the probabilities in the
distribution must sum to 1.
Section 4.1
 Example
1:
Construct a probability distribution for
rolling a single die.
Step 1: Determine the sample space
Step 2: Determine the probability for each
outcome.
Step 3: Construct the probability
distribution.
Section 4.1
 Example
2:
Represent graphically the probability
distribution for getting heads when tossing
three coins.
Step 1: Determine the sample space
Step 2: Determine the probability for each
outcome.
Step 3: Construct the probability
distribution.
Step 4: Construct your graph
Section 4.1
Things to remember…

Outcomes will be listed on your x-axis.

Probabilities will be listed on your y-axis.

You do not have to start your outcomes with 0
or on the origin.

Your probabilities will sum to 1.

Each probability must be between 0 and 1.
Section 4.1

Example 3:
During the summer months, a rental agency
keeps track of the number of chainsaws it rents each
day during a period of 90 days. The number of saws
rented per day is represented by the variable X. The
results are shown below:
X
# of Days
0
45
1
30
2
15
Total:
90
Compute the probability P(X) for each X, and construct
a probability distribution and graph for the data.
Section 4.1

a)
b)
c)
d)
Example 4:
Determine if each distribution is a probability
distribution. If not, state why.
X
0
5
10
15
20
P(x)
1/5
1/5
1/5
1/5
1/5
X
1
2
3
4
P(x)
1/4
1/8
1/16
9/16
X
0
2
4
6
P(x)
-1.0
1.5
0.3
0.2
X
2
3
7
P(x)
0.5
0.3
0.4
Section 4.1
Homework:
 Pg.
197 – 198 (9 - 27 ODD)