The document provides an overview of probability distributions for discrete random variables, highlighting their properties and illustrating how to construct them. Key objectives include understanding that probabilities must be between 0 and 1 and sum to 1 for validity. Several examples and exercises are included to reinforce the concepts presented.

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Lesson 1.3
Probability
Distributio
n

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Go as
One!

3. At the end of the lesson, the learners should be able
to illustrate a probability distribution for a discrete
random variable and its properties (M11/12SP-IIIa-4).

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Objectives
●Illustrate a probability distribution
for a discrete random variable.
●Construct a probability distribution
for a discrete random variable.

5. A probability distribution of a discrete
random variable is a list, a table, a graph,
or a formula of probabilities associated
with each of its possible values.
Probability Distribution of a Discrete Random
Variable

6. Properties:
• The probability of each outcome is between 0
and 1, inclusive. This means that .
• The sum of all the probabilities of the random
variable is equal to 1 or 100%. That is, .
Probability Distribution of a Discrete Random
Variable

7. Example 1: Determine whether the
distribution is a valid probability distribution
for a discrete random variable .

8. To determine whether a probability distribution is
valid, we must satisfy the two properties for the
probability distribution of a discrete random
variable.
1. The probability of each outcome is between
and.
The probabilities , and are all between and ,
inclusive.

9. 2. The sum of all the probabilities
of the random variable is equal
to or .
The sum of all the probabilities is 1.

10. Thus, the distribution is a valid
probability distribution for the discrete
random variable .

11. Example 2: Construct the probability
distribution for the random variable
which pertains to the number of tails
in each outcome when tossing two
coins.

12. Example 2: Construct the probability distribution for the random variable
which pertains to the number of tails in each outcome when tossing two
coins.
In tossing two coins, the possible outcomes are
where represents head and represents tail.
Solution

13. From the outcomes, we can have the following table:
Example 2: Construct the probability distribution for the random variable
which pertains to the number of tails in each outcome when tossing two
coins.
Solution
Number of tails Outcomes
,

14. Based on the table above, the random variable can take
the values of and
Example 2: Construct the probability distribution for the random variable
which pertains to the number of tails in each outcome when tossing two
coins.
Solution

15. Thus, the probability distribution for the discrete random
variable is
Example 2: Construct the probability distribution for the random variable
which pertains to the number of tails in each outcome when tossing two
coins.
Solution

16. Individual Practice:
1. Determine whether the distribution is a valid
probability distribution for a discrete random variable .

17. Individual Practice:
2. Consider the random experiment of rolling a pair of
tetrahedron dice (whose number of dots are to ).
Construct the probability distribution for the random
variable which denotes the sum of the numbers in the
two dice.

18. Group Practice: To be done in groups of three.
A bowl contains five marbles numbered as and. If a
random experiment of picking three marbles at a time was
conducted, construct a probability distribution for the
random variable which represents the sum of the numbers
on the marbles.

19. ● The probability distribution of a discrete random
variable is a list, a table, a graph, or a formula of
probabilities associated with each of its possible values.

20. ●Properties of a Probability Distribution:
a. The probability of each outcome is between 0 and 1,
inclusive. This means that .
b. The sum of all the probabilities of the random variable
is equal to 1 or 100%. That is, .

21. “Discrete Random Variables.” Lumen Learning. Retrieved 21 June 2019 from
https://courses.lumenlearning.com/boundless-statistics/chapter/discrete-random-variables/
Mendenhall III, William et al. Introduction to Probability and Statistics. United States of America: Cengage
Learning, 2013.
“Probability Distributions for Discrete Random Variables." Saylor Academy. Retrieved 21 June 2019
from
https://saylordotorg.github.io/text_introductory-statistics/s08-02-probability-distributions-for-.html

22. “Probability Distributions for Discrete Random Variables." Statistics LibreTexts. Retrieved 21 June 2019
from
https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Introductory_Statistics_(S
hafer_and_Zhang)/04%3A_Discrete_Random_Variables/4.02%3A_Probability_Distributions_for_Discr
ete_Random_Variables
“Random Variable and Its Probability Distribution.” Toppr. Retrieved 21 June 2019 from
https://www.toppr.com/guides/maths/probability/random-variable-and-its-probability-distribution/