1. Unit 5
Section 5-2

2. 5-2: 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.

3. Section 5-2
Discrete Probability Distribution – consists of the values a random variable can assume and the corresponding probabilities of values.
The probabilities are determined theoretically or by observation.

4. Section 5-2
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.

5. Section 5-2
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

6. Section 5-2 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 on the origin.
Your probabilities will sum to 1.
Each probability must be between 0 and 1.

7. Section 5-2
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:
Compute the probability P(X) for each X, and construct a probability distribution and graph for the data. X
# of Days 45 1 30 2 15
Total: 90

8. Section 5-2
Example 4:
Determine if each distribution is a probability distribution. If not, state why. a) b) c) d) X 5 10 15 20
P(x)
1/5 X 1 2 3 4
P(x)
1/4
1/8
1/16
9/16 X 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

9. Section 4-5
Homework:
Pg 244 – 245: EVEN, EVEN