STATISTICS

1. Lesson 4
Solving Random
Variables

2. Objectives
At the end of this lesson, the learner should be able to
● accurately solve possible values of a random
variable; and
● correctly solve real-life problems involving the
random variables.

3. Essential Questions
● How do you solve for the possible values of a random
variable?
● What is the relationship of probability in solving for
possible values of a random variable?
● How are you able to solve problems involving random
variables?

4. Warm Up!
Before we learn about solving random variables, let us have a
short game where I will ask questions/pick up dares to
chosen students using the online wheel.
(Click on the link to access the online wheel.)
“Wheel Decide.” Wheel Decide. Retrieved 24 June 2019 from
https://wheeldecide.com/.

5. Guide Questions
● Do you think the wheel randomly chose names?
● Do you have the control to pick your name in the wheel?
● What are the chances that your name will be chosen?

6. Learn about It!
Discrete Random Variable
is a random variable with a finite number of possible values or an infinite number
of values that can be counted
1
Example:
The number of pupils, number of pencils, cards in a standard
deck are examples of a discrete random variable since it can
be counted as 0, 1, 2, 3, and so on. It has an infinite number of
values that can be counted.

7. Try It!
Example 1:
Given the probability distribution of a discrete random
variable 𝑋 below, find 𝑃(𝑋 = 3).
𝑿 1 2 3 4
𝑷(𝑿) 0.10 0.21 ? 0.5

8. Try It!
Example 1:
Given the probability distribution of a discrete random
variable 𝑋 below, find 𝑃(𝑋 = 3).
Solution:
In a probability distribution for a discrete random variable, the
sum of all the probabilities of the outcomes should be equal to
1. That is 𝑃 𝑋 = 1.
𝑿 1 2 3 4
𝑷(𝑿) 0.10 0.21 ? 0.5

9. Try It!
Example 1:
Given the probability distribution of a discrete random
variable 𝑋 below, find 𝑃(𝑋 = 3).
Solution:
Add all the probabilities and equate it to 1 to find the missing
value.
𝑃 𝑋 = 1 + 𝑃 𝑋 = 2 + 𝑃 𝑋 = 3 + 𝑃 𝑋 = 4 = 1
𝑿 1 2 3 4
𝑷(𝑿) 0.10 0.21 ? 0.5

10. Try It!
Example 1:
Given the probability distribution of a discrete random
variable 𝑋 below, find 𝑃(𝑋 = 3).
Solution:
0.10 + 0.21 + 𝑃 𝑋 = 3 + 0.5 = 1
0.81 + 𝑃 𝑋 = 3 = 1
𝑃 𝑋 = 3 = 1 − 0.81
𝑃 𝑋 = 3 = 0.19
Thus, 𝑷 𝑿 = 𝟑 = 𝟎. 𝟏𝟗.
𝑿 1 2 3 4
𝑷(𝑿) 0.10 0.21 ? 0.5

11. Try It!
Example 2:
Given the probability distribution of a discrete random
variable 𝑋 below, find 𝑃(𝑋 < 3).
𝑿 1 2 3 4
𝑷(𝑿) 1
10
3
10
2
10
4
10

12. Try It!
Example 2:
Given the probability distribution of a discrete random
variable 𝑋 below, find 𝑃(𝑋 < 3).
𝑿 1 2 3 4
𝑷(𝑿) 1
10
3
10
2
10
4
10
Solution:
Analyze the problem.
The notation 𝑃(𝑋 < 3) means that the random variable 𝑋 is less
than 3.

13. Try It!
Example 2:
Given the probability distribution of a discrete random
variable 𝑋 below, find 𝑃(𝑋 < 3).
𝑿 1 2 3 4
𝑷(𝑿) 1
10
3
10
2
10
4
10
Solution:
The random variables take on the values 1, 2, 3, and 4 in which 1
and 2 are less than 3. The probabilities are 𝑃(𝑋 = 1) and 𝑃(𝑋 =
2). Add all the identified probabilities.
𝑃 𝑋 < 3 = 𝑃 𝑋 = 1 + 𝑃 𝑋 = 2

14. Try It!
Example 2:
Given the probability distribution of a discrete random
variable 𝑋 below, find 𝑃(𝑋 < 3).
𝑿 1 2 3 4
𝑷(𝑿) 1
10
3
10
2
10
4
10
Solution:
𝑃 𝑋 < 3 = 𝑃 𝑋 = 1 + 𝑃 𝑋 = 2
𝑃 𝑋 < 3 =
1
10
+
3
10
=
4
10
or
2
5
Therefore, the probability that the random variable 𝑋 is less
than 3 is
𝟒
𝟏𝟎
or
𝟐
𝟓
.

15. Let’s Practice!
Individual Practice:
1. Below is a valid probability distribution of a random
variable 𝑋. Solve for the missing value.
𝑿 3 5 6 9
𝑷(𝑿) 1
5
𝑘 2
10
2𝑘

16. Let’s Practice!
Individual Practice:
2. Given the probability distribution of a discrete random
variable 𝑋 below, find 𝑃(𝑋 ≥ 78).
𝑿 77 78 79 80 81
𝑷(𝑿) 0.135 0.292 0.284 0.230 0.059

17. Let’s Practice!
Group Practice: The class will be divided into 5 groups.
The number of hours that a student spends in studying at
home is a random variable 𝑋 given by 𝑃 𝑋 =
𝑥+2
9
, where
𝑥 = 0, 1, and 2.
a. Construct the probability distribution for the random
variable 𝑋.
b. What is the probability that a student spent at least 1 hour
studying at home?

18. Key Points
Discrete Random Variable
is a random variable with a finite number of possible values or an infinite number
of values that can be counted.
1

19. Synthesis
● How do we solve possible values of a random variable?
● How are random variables applicable in our daily lives?
Can you give a specific example?
● How do you know the outcome that will most likely to
happen?