This document provides information about random variables. It begins by defining a random variable as a numerical quantity that results from a random experiment. Random variables can be discrete if they have countable possible outcomes, or continuous if their possible values contain a whole interval of numbers. The document then discusses key properties of random variables, such as that they take on exactly one value for each random outcome and are conceptually different from mathematical variables. It provides examples of how random variables can model real-world outcomes that cannot be predicted with certainty in advance. The document goes on to classify examples as having discrete or continuous distributions and illustrates finding the possible values of random variables through examples.
1. Definition
Random Variable
A numerical quantity that is generated by a
random experiment.
• It could be discrete if it has a finite or
countable number of possible outcomes that
can be listed.
• Continuous if its possible values contain a
whole interval of numbers.
2. About Random Variables
That a random variable must take exactly one value for
each random outcome.
That random variables are conceptually different from
the mathematical variables that they have met before in
math classes. A random variable is linked to observations
in the real world, where uncertainty is involved.
Random variables are used to model outcomes of random
processes that cannot be predicted deterministically in
advance (the range of numerical outcomes may, however
be viewed).
3. The average
weight of new
born babies in the
2020
Getting the
distance travelled
by a car
Tallying the number
of PUI (Person
Under Investigation)
due to Covid-19
pandemic.
The speed of bus
The temperature in
Quezon at noon
times
Classify the following variables as discrete or continuous.
Write D if discrete and C if continuous.
Collecting data about the
weights of students in a
certain school
01 02 03
05 06 07
The average
temperature of the
costumers in a
department store last
week as reflected in
the logbook
Picking a multiple
of 3 less than 200
04
08
5. A certain area in the Southern part of Negros Oriental
experienced black out. A couple, having a new born baby, found
difficulty putting their baby to sleep when there is no electricity. The
couple has two (2) Mini 12v rechargeable hybrid car batteries. They
thought of using it to at least put up a single light bulb. To make sure
that both are functioning well they need to test them randomly first.
Thus, to each outcome in the sample space we shall assign a value.
These are 0, 1, or 2. If there is no defective, we assign the number 0;
if there is 1 defective, we assign the number 1; and 2, if there are two
defective batteries. The number of defective batteries is a random
variable. The possible values of this random variable are 0, 1, and 2.
6. Let D represent the defective battery and N for the non-
defective. If we let Y be the random variable representing
the number of defective battery, show the values of the
random variable Y. Complete the table below to show the
values of the random variable.
Possible Outcomes Value of the Random Variable Y
(number of defective battery)
7. Let D represent the defective battery and N for the non-
defective. If we let Y be the random variable representing
the number of defective battery, show the values of the
random variable Y. Complete the table below to show the
values of the random variable.
Possible Outcomes Value of the Random Variable Y
(number of defective battery)
DD 2
NN 0
ND 1
DN 1
8. Suppose three laptops are tested at random. We want to find
out the number of non-defective laptops. Thus, to each outcome
in the sample space we shall assign a value. These are 0, 1, 2, or
3. If there is no defective laptop, we assign the number 0; if
there is 1 non-defective, we assign the number 1; if there are 2
non-defective laptops, we assign the number 2; and assign 3 if
there are 3 non-defective laptops. If we let X be the random
variable representing the number of non-defective laptops,
show the values of the random variable X.
9.
10. EXAMPLE 1
In a box are 2 balls - one white and one yellow. Two balls are picked
one at a time with replacement. Let X be the random variable
representing the number of white balls. Find the values of the random
variable X.
11. EXAMPLE 2
Suppose two coins are tossed, let Z be the random variable
representing the number of heads that occur. Find the values of the
random variable Z.
12. Independent Assessment 1
Understanding Possible Values of Random Variables. Answer
the following questions.
1. How do you find the values of a random variable?
2. How is this variable, as described in Algebra, similar to a
random variable? How do they differ?
13. Independent Assessment 2
Four coins are toss. Let Y be the random variable representing
the number of tails that occur. Find the values of the random
variable Y.
15. In your previous lesson, you have learned how to find the possible values of
a random variable. In this new lesson, you will learn how to illustrate a
probability distribution of a discrete random variable. To find out if you are
ready to learn in this new lesson, answer the following questions.
Determine whether the statement is True or False. If the answer is false, you can
modify the statement to make it true.
16. Number of Defective
Computers
03
In a computer laboratory, the teacher wants to find out if there is
a defective computer. Supposed three computers were tested at
random, she asks one of her Computer System Servicing
students to list all the possible outcomes, such that D represents
the defective computer and N represents the non-defective
computer. Let X be the random variable for the number of
defective computers. Then, illustrate the probability distribution of
the random variable X.
17. TABLE OF CONTENTS
MOST AND
LEAST LIKELY
02
CHAPTER
TEST
03
CERTAIN OR
IMPOSSIBLE
01
You can describe
the topic of the
section here
You can describe
the topic of the
section here
You can describe
the topic of the
section here
18. 01
You can enter a subtitle here if you need it
CERTAIN OR IMPOSSIBLE?
19. CERTAIN
Venus is the second
planet from the Sun
LIKELY
Mercury is the smallest
planet of them all
UNLIKELY
Despite being red, Mars
is actually a cold place
IMPOSSIBLE
Saturn is a gas giant and
has several rings
DEFINE CONCEPTS
20. JUPITER
Jupiter is a gas giant and
the biggest planet in the
Solar System VENUS
Venus has a beautiful
name and is the second
planet from the Sun
MARS
Despite being red, Mars is
actually a cold place. It’s
full of iron oxide dust
FEATURES OF THE TOPIC
21. PROBLEM SOLUTION
Earth is the third planet from the Sun
and the only one that harbors life in
the Solar System. This is where we
all live
Despite being red, Mars is actually a
cold place. It's full of iron oxide dust,
which gives the planet its reddish
cast
PROBLEM VS. SOLUTION
26. It’s the biggest planet in
the Solar System
VENUS
Venus is the second
planet from the Sun
MARS
Despite being red, Mars
is a cold place
JUPITER
SATURN
Saturn is a gas giant
and has several rings
MOST AND LEAST LIKELY
27. PROBABILITY STEP BY STEP
Saturn has high
temperatures
Jupiter is the
biggest planet
STEP 2 STEP 4
Venus is a
beautiful place
Mars is red and
a cold place
STEP 1 STEP 3
28. POSSIBLE
CERTAIN IMPOSSIBLE
Mercury is the smallest
planet of them all
Venus has extremely
high temperatures
Earth is the only planet
that harbors life
99% 50% 1%
DID YOU KNOW THIS?
30. Images reveal large amounts of data, so
remember: use an image instead of a long
text. Your audience will appreciate it
AN IMAGE
REINFORCES
THE CONCEPT
31. PROBABILITY IN OUR LIFE
EXAMPLES
CERTAIN
● The Sun will rise
tomorrow morning
● You’ll dinner tonight with
your family
LIKELY
● Ms. Vant will teach
Science next year
● You’ll visit your parents
on the weekend
IMPOSSIBLE
● Ms. Jhon will be
president in 2080
● You’ll turning back into a
baby in ten years
32. EXERCISE 01
If you select a marble without looking, which color are you more likely to choose?
A Yellow
B Red
Put the following mark in the correct answer:
33. EXERCISE 02
If you select a marble without looking, the color you
are unlikely to choose would be:
You can write your answer here
34. EXERCISE 03
There is a box full of colored balls...If you choose a ball without
looking, which one are you least likely to catch?
YELLOW BALLS ORANGE BALLS PINK BALLS
You can write your answer here
35. EXERCISE 04
How likely is it that the spinner will land on…?
Put the following mark in the correct answer:
RED PINK BLUE
Certain
Likely
Unlikely
Impossible
36. KNOWLEDGE PROGRESS
MERCURY
It is the closest
planet to the Sun
VENUS
It is the second
planet from the Sun
NEPTUNE
It’s the farthest
planet from the Sun
30% 50%
70%
SATURN
It is a gas giant and
has several rings
90%
Follow the link in the graph to modify its data
and then paste the new one here. For more
info, click here
37. THIS IS A MAP
Despite being
red, Mars is a
cold place
VENUS
Venus is the
second planet
from the Sun
JUPITER
Jupiter is the
biggest planet
of them all
MARS SATURN
Saturn is a gas
giant and has
several rings
38. JENNA DOE SUSAN BONES
You can talk a bit about this
person here
You can talk a bit about this
person here
OUR TEACHERS
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2016 2017 2018 2019 2020
“Despite being red,
Mars is actually a
very cold place”
“Mercury is closest
planet to the Sun
and the smallest”
“Neptune is the
farthest-known
planet from the Sun”
“Saturn is a gas
giant and has
several rings”
“Venus is the
second planet from
the Sun and is
terribly hot”
Premium infographics
63. “Mercury is closest
planet to the Sun
and the smallest”
TITLE 1
75% “Mercury is closest
planet to the Sun
and the smallest”
“Mercury is closest
planet to the Sun
and the smallest”
“Mercury is closest
planet to the Sun
and the smallest”
75%
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