Random variable

1. RANDOM VARIABLE

2. Learning Competencies
The learner will be able to:
illustrate a random variable
(discrete and continuous);
distinguish between a discrete
and a continuous variable; and
find the possible values of a
random variable.

3. ORAL EXERCISES
Describe each of the given images.

4. ORAL EXERCISES
Determine the possible
outcomes of the given
experiment.
1. Tossing a coin
2. Rolling a die
3. Tossing two coins
4. Rolling two dice
5. Rolling a die and tossing a

5. STATISTIC
S
It is a branch of applied
mathematics that deals with the
collection, organization,
presentation, analysis and
interpretation of data.

6. PROBABILIT
Y
It is a mathematical concept that is
used to measure the certainty or
uncertainty of occurrence of
statistical phenomena.

7. Two Kinds of Statistics
 DESCRIPTIVE
STATISTICS
It deals with the
collection and
presentation of data
and the
summarizing values
that describes the
group’s
characteristics.
 INFERENTIAL
STATISTICS
It deals with
predictions and
inferences based
on the analysis and
interpretation of the
results of the
information
gathered by the
statistician.

8. VARIABLE
It is a numerical characteristics or
attribute associated with the
population being studied.

9. Two Types of Variables
 CATEGORICAL
OR
QUALITATIVE
VARIABLES
These are variables
that are classified
according to some
attributes or
categories.
 NUMERICAL-
VALUED OR
QUANTITATIVE
VARIABLES
These are variables
that are classified
according to
numerical
characteristics.

10. RANDOM
VARIABLE
It is a variable whose possible
values are determined by chance. It
is a set whose elements are the
numbers assigned to the outcomes
of an experiment. It is a function that
associates a real number to each
element in the sample space. It is a
variable whose values are
determined by chance.

11. Types of Random Variables
DISCRETE RANDOM
VARIABLE
A random variable that has a finite
number elements or infinite but can
be represented by whole numbers.
These values usually arise from
counts.

12. Examples:
 Let X = number of students
randomly selected to be interviewed
by a researcher.
 Let Y = number of left-handed
teachers randomly selected in a
faculty room.
 Let Z = number of defective light
bulbs among the randomly selected
light bulbs.

13. Types of Random Variables
CONTINUOUS RANDOM
VARIABLE
A random variable that has an
infinite number elements but cannot
represented by whole numbers.
These values usually arise from
measurements.

14. Examples:
 Let Y = the weights of randomly
selected students in pounds.
 Let X = the lengths of randomly
selected shoes of senior students in
centimeters.
 Let Z = the hourly temperature daily.

15. ACTIVITY 1
Determine if the random variable X or Y is
discrete or continuous.
a. X = number of points scored in the last
season by a randomly selected basketball
player in the PBA.
b. Y = the height of a randomly selected
student inside the library in centimeter.
c. X = number of birds in a nest.
d. Y = the weights in kg of randomly selected
dancers after taking up aerobics.
e. X = the heights of daisy plants in the
backyard.

16. SAMPLE
SPACE
It is the set of all possible outcomes
of an experiment.

17. DISTINCT VALUES
These are exact values and can
be represented by nonnegative
whole numbers.

18. Illustration:
1. Suppose three cell phones are tested
at random. Let D represent the
defective cell phone and N represent
the non-defective cell phone. If we let X
be the random variable representing the
number of defective cell phone, show
the values of the random variable X?
Possible Outcomes Values of the Random Variable X
(number of defective cell phones)

19. Illustration:
2. Suppose three coins are tossed. Let
Y be the random variable representing
the number of tails that occur. Find the
values of the random variable Y.
Complete the table below.
Possible Outcomes Values of the Random Variable Y
(number of tails)

20. Illustration:
3. Two balls are drawn in succession
without replacement from an urn
containing 5 red balls and 6 blue balls.
Let Z be the random variable
representing the number of blue balls.
Find the values of the random variable
Z. Complete the table below.
Possible Outcomes Values of the Random Variable Z
(number of blue balls)

21. ACTIVITY 2
Find the value of the random variable.
Four coins are tossed. Let Z be the
random variable representing the
number of heads occur. Find the values
of the random variable Z.
Possible Outcomes Values of the Random Variable
Z
(number of heads)

22. GENERALIZATION
Answer the following questions.
1. Define random variable.
2. How do you know whether a random
variable is continuous or discrete?
3. What is the difference between
continuous and discrete random
variables?
4. How do you find the values of a
random variable?