This document outlines the process of calculating the mean of a discrete probability distribution, including objectives, examples, and exercises. It explains that the mean is a weighted average of possible values and provides examples such as rolling a die and grocery item purchases. The document emphasizes constructing a probability distribution, multiplying values by probabilities, and summing the results to find the mean.

1. COMPUTING THE MEAN OF A DISCRETE
PROBABILITY DISTRIBUTION

2. Lesson Objectives
At the end of this lesson, you are expected 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. Pre-Assessment A
Recap: Evaluating Summations

4. Pre-Assessment B
Recap:
Finding the mean of a data set.

5. Lesson Introduction
Mathematicians usually consider the outcomes
of a coin toss as a random event. That is, each
probability of getting a head is 12 , and the
probability of getting a tail is 12 .
However, it is not possible to predict with
100% certainty which outcome will occur.

6. Discussion Points
The mean of a discrete random variable X is the
weighted average of the possible values that the
random variable can take.

7. Discussion Points
Illustrative Example:
Consider rolling a die. What is the average
number of spots that would appear?

8. Discussion Points
Step 1.
Construct the probability distribution for the
random variable X representing the number of
spots that would appear.
Number of Spots X Probability P(X)
1 1/6
2 1/6
3 1/6
4 1/6
5 1/6
6 1/6

9. Discussion Points
Step 2.
Multiply the value of the random variable X by the
corresponding probability.

10. Discussion Points
Step 3:
Add the results obtained in Step 2.
The mean tells us the average number of spots that would appear in a
roll of a die. So, the average number of spots that would appear is 3.5.
Although the die will never show a number, which is 3.5, this implies
that rolling the die many times, the theoretical mean would be 3.5.

11. Discussion Points

12. Example 1
Grocery Items
The probabilities that a customer will buy 1, 2, 3,
4, or 5 items in a grocery store
are 3/10, 1/10, 1/10, 2/10, and 3/10,
respectively. What is the average number of
items that a customer will buy?

13. Solution to Example 1
Step 1.
Construct the
probability
distribution for the
random variable X
representing the
number of items
that the customer
will buy.

14. Solution to Example 1
Step 2:
Multiply the value of the random variable X by the
corresponding probability.

15. Solution to Example 1
Step 3:
Add the results obtained in Step 2.
The mean of the probability distribution is 3.1. This implies that the
average number of items that the customer will buy is 3.1.

16. Example 2
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.

24. Solution to Example 2
Step 1:
Construct the probability distribution for the random
variable X representing the number of patients that a
surgeon operates on a day.
Number of Patients X Probability P(X)
3 0.15
4 0.10
5 0.20
6 0.25
7 0.30

25. Solution to Example 2
Step 2:
Multiply the value of the random variable X by the
corresponding probability.
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

26. Solution to Example 2
Step 3:
Add the results obtained in Step 2.
The average number of patients that a surgeon will operate
in a day is 5.45.

27. Exercise 1 Complete the table below and find the mean of the following probability
distribution.

28. Exercise 2
Find the mean of the probability distribution of
the random variable X, which can take only the
values 1, 2, and 3, given that P(1) = 10/33, P(2) =
1/3 , and P(3) = 12/33.
Exercise 3
The probabilities of a machine manufacturing 0,
1, 2, 3, 4, or 5 defective parts in one day are 0.75,
0.17, 0.04, 0.025, 0.01, and 0.005, respectively.
Find the mean of the probability distribution.

29. Exercise 4
A bakeshop owner determines the number of boxes of
pandesal that are delivered each day. Find the mean of the
probability distribution shown. If the manager stated that 35
boxes of pandesal were delivered in one day, do you think
that this is a believable claim?
Number of Boxes X Probability P(X)
35 0.10
36 0.20
37 0.30
38 0.30
39 0.10

30. Summary
The mean of a discrete random variable X is
the weighted average of the possible values
that the random variable can take.

31. Summary
To find the mean of the probability
distribution,
• Construct the probability distribution for
the random variable X
• Multiply the value of the random variable
X by the corresponding probability.
• Add the results obtained in Step 2.