Lesson 2 – Probability Distribution
CONTEXT
Learning Competencies:
After the lesson, the learner can:
a. illustrate probability distribution for a discrete random variable and its
properties;
b. construct the probability mass function of a discrete random variable and its
corresponding histogram;
c. compute probabilities corresponding to a given random variable;
Values Integration: In this lesson, students develop competence and ethical
reasoning by analyzing data patterns, interpreting distributions, making logical
predictions based on probabilities, and using probability responsibly to ensure fairness
and unbiased representation in real-life applications such as statistics and decision
making.
Essential Understanding: Probability distributions describe how the outcomes of
a random variable are spread across possible values. They provide a framework for
understanding uncertainty, predicting outcomes, and making data-driven decisions in
various real-world contexts. By mastering probability distributions, students gain the
ability to interpret, model, and solve problems involving randomness and variability.
EXPERIENCE
Prelection
Activity 2.1
Instructions: In the previous lesson, you learned about random variables and mass
points. In this exercise, identify the mass points and the total number of possible
outcomes for each of the given discrete random variables.
Random Variables Mass Total
Points Possible
Outcomes
1. H = the number of heads when two coins are tossed
2. S = the sum of the numbers when two dice are rolled
3. M = number of males when 2 students are chosen
at random from a group with 2 males and 3 females
13
, Concept Notes
Probability Distribution
It is the set of all mass points with their corresponding probabilities.
Example 2.1
Express the probability distribution for the random variable in a tabular form.
H = the number of heads when two coins are tossed
We have,
Mass Point Probabilities
Recall that, in general, the probability
ℎ ��(ℎ)
of a random variable, X is
0 1/4
�� �� =������������ ����
1 2/4 or ½ ����������
���������� ������������
2 1/4 ���� ��������������
Note: In some references, it can also be denoted as ��(�� = ��).
Types of Probability Distribution
Probability Mass Function (PMF)
▪ It is a probability measure that gives us probabilities of the possible value for
discrete random variables.
▪ It is expressed in tabular, graphical, and formula forms.
Probability Density Function (PDF)
▪ It is a probability measure that gives us probabilities of the possible value for
continuous random variables.
▪ It is expressed in graphical and formula forms.
PROPERTIES OF PROBABILITY DISTRIBUTION
▪ Non-negativity Property – there are no negative probabilities
0 ≤ �� �� ≤ 1 or 0% ≤ �� �� ≤ 100%
▪ Norming Property – the total probability is 1 or 100%
σ ��(��) = 1 or σ ��(��) = 100%
CONTEXT
Learning Competencies:
After the lesson, the learner can:
a. illustrate probability distribution for a discrete random variable and its
properties;
b. construct the probability mass function of a discrete random variable and its
corresponding histogram;
c. compute probabilities corresponding to a given random variable;
Values Integration: In this lesson, students develop competence and ethical
reasoning by analyzing data patterns, interpreting distributions, making logical
predictions based on probabilities, and using probability responsibly to ensure fairness
and unbiased representation in real-life applications such as statistics and decision
making.
Essential Understanding: Probability distributions describe how the outcomes of
a random variable are spread across possible values. They provide a framework for
understanding uncertainty, predicting outcomes, and making data-driven decisions in
various real-world contexts. By mastering probability distributions, students gain the
ability to interpret, model, and solve problems involving randomness and variability.
EXPERIENCE
Prelection
Activity 2.1
Instructions: In the previous lesson, you learned about random variables and mass
points. In this exercise, identify the mass points and the total number of possible
outcomes for each of the given discrete random variables.
Random Variables Mass Total
Points Possible
Outcomes
1. H = the number of heads when two coins are tossed
2. S = the sum of the numbers when two dice are rolled
3. M = number of males when 2 students are chosen
at random from a group with 2 males and 3 females
13
, Concept Notes
Probability Distribution
It is the set of all mass points with their corresponding probabilities.
Example 2.1
Express the probability distribution for the random variable in a tabular form.
H = the number of heads when two coins are tossed
We have,
Mass Point Probabilities
Recall that, in general, the probability
ℎ ��(ℎ)
of a random variable, X is
0 1/4
�� �� =������������ ����
1 2/4 or ½ ����������
���������� ������������
2 1/4 ���� ��������������
Note: In some references, it can also be denoted as ��(�� = ��).
Types of Probability Distribution
Probability Mass Function (PMF)
▪ It is a probability measure that gives us probabilities of the possible value for
discrete random variables.
▪ It is expressed in tabular, graphical, and formula forms.
Probability Density Function (PDF)
▪ It is a probability measure that gives us probabilities of the possible value for
continuous random variables.
▪ It is expressed in graphical and formula forms.
PROPERTIES OF PROBABILITY DISTRIBUTION
▪ Non-negativity Property – there are no negative probabilities
0 ≤ �� �� ≤ 1 or 0% ≤ �� �� ≤ 100%
▪ Norming Property – the total probability is 1 or 100%
σ ��(��) = 1 or σ ��(��) = 100%
