SP Lesson 1.pptx_statistics and probability

Give your insights
about the word
“Random”

In statistics, when
we say random, it
has something to
do with probability
or chances.

Lesson 1.1
Introduction to Random
Variables

Learning Competency
At the end of the lesson, the learners should
be able to do the following:
● Illustrate a random variable (discrete and
continuous) [M11/12SP-IIIa-1].

Objectives
1. Define a random variable.
2. Cite real-life situations using random
variables.

Check-up Questions:
Directions:
1. Fill in the KW chart
2. Indicate what you know about the subject and what
you want to know about Statistics and Probability.
3. Random students will present the output.
Group Activity

Check-up Questions:
1. How did you find the activity class?
2. What have you realized after accomplishing the
activity?
3. Why is there a need to study Statistics and
Probability?

Learn about It!
A random experiment is an experiment that can be
repeated numerous times under the same conditions.
The results must be independent of one another.
Example:
Tossing a coin is a random experiment.
Random Experiment

Learn about It!
An outcome is the result of a random
experiment.
Example:
The possible outcomes of tossing a coin are
head and tail.
Outcome

Learn about It!
A sample space
is the set of possible outcomes
of a random experiment; denoted by a capital
letter, usually .
Example:
The sample space of tossing a coin is .
Sample Space

Learn about It!
A random variable is a function that associates a
numerical value to every outcome of a random
experiment; denoted by a capital letter, usually .
The domain is the sample space, and the range is
some set of real numbers.
Random Variables

Learn about It!
Example:
Suppose represents the number of heads that
can appear in tossing a coin. The possible values
of the random variable are 0 and 1.
Random Variables

Try it!
Let’s Practice
Example 1: Let be a random variable that denotes the result
of rolling a die. What are the possible values of ?

Solution to Let’s Practice
Example 1: Let be a random variable that denotes the result
of rolling a die. What are the possible values of ?
Solution:
The sample space of rolling a die is Thus, the possible values
of are and .

Try it!
Let’s Practice
Example 2: A coin is flipped three times. If represents the
number of tails of the outcome, what are the possible values
of ?

Solution:
1. List the possible outcomes of the experiment.
Example 2: A coin is flipped three times. If represents the number of tails of
the outcome, what are the possible values of ?
This can be done using a table or tree diagram. Let
represent heads and represent tails.

Solution:

Solution:
From the illustration on the previous slide, we can say
that the possible outcomes are:
𝑆={𝐻𝐻𝐻,𝐻𝐻𝑇 ,𝐻𝑇𝐻,𝐻𝑇𝑇 ,𝑇𝐻𝐻,𝑇𝐻𝑇,𝑇𝑇𝐻,𝑇𝑇𝑇}

Solution:
2. Count the number of tails in each outcome.
Possible
outcomes
Number of tails Possible
outcomes
Number of tails
HHH 0 THH 1
HHT 1 THT 2
HTH 1 TTH 2
HTT 2 TTT 3

Solution:
2. Count the number of tails in each outcome.
Based on the table, the number of tails can be , , , or .
Thus, the possible values of are and.

Group Activity
●Cite real-life situations using random
variables. Associate a numerical value to
every outcome of a random experiment;
denoted by a capital letter .
𝑋

Essay Test
Direction: Cite real-life situations using random
variables.

SP Lesson 1.pptx_statistics and probability

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