Statistics and Probability

1. Computing the Mean
of a Discrete
Probability Distribution

2. Lesson Objectives
At the end of this lesson, you should be able to:
• illustrate and calculate the mean of a discrete
random variable;
• interpret the mean of a discrete random variable;
and
• solve problems involving mean of probability
distributions.

3. Content
• Entry Card: Summation
• Sample Problem 1: Number of Spots
• Formula for the Mean of the Probability Distribution
• Sample Problem 2: Grocery Items
• Sample Problem 3: Surgery Patients
• Seatwork
• Enrichment
• Assessment

4. Entry Card
Given the values of the variables X and Y, evaluate the
following summations.
1. 2.
3. 4.
5.

5. Problem 1: Number of Spots
Consider rolling a die. What is the average number of spots
that would appear?
Solution:
Step 1: Construct the probability distribution for the random
variable X representing the number of spots that would
appear.
Step 2: Multiply the value of the random variable X by the
corresponding probability.
Step 3: Add the results obtain in Step 2.

6. Step 1
Number of Spots X Probability P(X)
1
2
3
4
5
6

7. Number of Spots X Probability P(X) X ∙ P(X)
1
2
3
4
5
6
Step 2

8. Step 3
Number of Spots X Probability P(X) X ∙ P(X)
1
2
3
4
5
6

9. Formula for the Mean of the
Probability Distribution
The mean of a random variable with a discrete probability
distribution is:
or
where:
are the values of the random variable X;
and
,,, …, are the corresponding probabilities.

10. Problem 2: Grocery Items
The probabilities that a costumer will buy 1, 2, 3, 4, or
5 items in a grocery store are , respectively. What is
the average number of items that a costumer will
buy?

11. Step 1
Number of Items X Probability P(X)
1
2
3
4
5

12. Number of Items X Probability P(X) X ∙ P(X)
1
2
3
4
5
Step 2

13. Step 3
Number of Items X Probability P(X) X ∙ P(X)
1
2
3
4
5

14. Problem 3: Surgery Patients
The probabilities that a surgeon operates on 3, 4, 5,
6, or 7 patients in any day are 0.15, 0.10, 0.20, 0.25,
and 0.30, respectively. Find the average number of
patients that a surgeon operates on a day.

15. Step 1
Number of Patients X Probability P(X)
3 0.15
4 0.10
5 0.20
6 0.25
7 0.30

16. Number of
Patients X
Probability P(X) X ∙ P(X)
3 0.15 0.45
4 0.10 0.40
5 0.20 1.00
6 0.25 1.50
7 0.30 2.10
Step 2

17. Step 3
Number of Patients X Probability P(X) X ∙ P(X)
3 0.15 0.45
4 0.10 0.40
5 0.20 1.00
6 0.25 1.50
7 0.30 2.10

18. Complete the table below and find the mean of the following
probability distribution.
E(x.Px)= 6.75
X P(X) X ∙ P(X)
3 0.15 0.45
6 0.35 2.10
8 0.40 3.20
10 0.10 1.00

19. X P(X) X ∙ P(X)
1 1/7
6 6/7
11 33/7
16 16/7
21 21/7 =77/7 or 11
2.

20. 3.
Number of Items X Probability P(X) X ∙ P(X)
1 4/9
3 2/3 or 6/9
5 5/9
7 14/9= 29/9 or 3.22

21. Find the mean of the probability distribution of the
random variable X, which can take only values 1, 2,
and 3, given that .
1 10/33 10/33
2 1/3 2/3
3 12/33 36/33
=68/33
or 2.06

23. Questions?
Clarifications?

24. Thank You for listening . . .