This document defines key concepts related to random variables including discrete vs. continuous variables and dependent vs. independent variables. It provides examples of each type of variable and discusses how to determine if a variable is discrete or continuous. The document also explains that a dependent variable's values are predicted based on an independent variable which is controlled in an experiment. It concludes with a formula for finding the possible values of a random variable by summing its values.

1. Random Variable
Statistics and Probability

2. Competencies:
• Illustrates a random variable (discrete and
continuous);
• Illustrates a random variable (dependent
and independent);
• distinguishes between a discrete and
continuous random variable and dependent
and independent variable; and
• Finds the possible values of a random
variable.

3. Definition:
Variable – object, person and characteristics of a
person under investigation.
Examples: height, weight, number of students,
behavior, etc.

4. Definitions:
Discrete variables
– can be
obtained by
counting
Examples:
Number of births, death,
marriages, number of
students in any given
period of time
Continuous variables
– obtained by
measurement
- can assume any
values
Examples:
Height, Weight, ages,
time, temperatures,
volumes, areas

5. Practice Activity
Determine if the following examples are
discrete or continuous variables.

6. Discrete or Continuous
• The number of boys in a randomly selected three-
child family.
Discrete
• The temperature of a cup of coffee served at a
restaurant.
Continuous
• The number of no-shows for every 100 reservations
made with a commercial airline.
Discrete

7. Discrete or Continuous
• The number of vehicles owned by a randomly
selected household.
Discrete
• The average amount spent on electricity each July by
a randomly selected household in a certain state.
Continuous

8. Definitions:
Dependent variable – values are
predicted
Independent variable – use to predict
the values

9. DEPENDENT VS. INDEPENDENT
• The independent variable is the one the
experimenter controls. The dependent
variable is the variable that changes in
response to the independent variable.
• The two variables may be related by cause
and effect. If the independent variable
changes, then the dependent variable is
affected.

10. Example 1:
Factors Affecting Academic
Performance of Grade 11 Students
Factors may include I.Q., study habits,
etc.

11. Example:
Factors Affecting Academic
Performance of Grade 11 Students
Factors may include I.Q., study habits,
etc.
Dependent
Variable
Independen
t Variable
Dependent
Variable
Independen
t Variable

12. Example 2:
Mr. S set up an experiment to see
how the mass of a ball affects the
distance it rolls off a ramp.

13. Example 2:
Mr. S set up an experiment to see
how the mass of a ball affects the
distance it rolls off a ramp.
Dependent
Variable
Independen
t Variable

14. Example 3:
Eating breakfast in the morning
increases the ability to learn in
school.

15. Example 3:
Eating breakfast in the morning
increases the ability to learn in
school.
Dependent
Variable
Independen
t Variable

16. Finding the Possible Values of a
Random Variable
FORMULA:
𝒊=𝟏
𝒏
Xi
…means the sum of X1, X2, … Xn.

17. References:
Retreived from:
https://stats.libretexts.org/Bookshelves/Introductor
y_Statistics/Book%3A_Introductory_Statistics_(Shaf
er_and_Zhang)/04%3A_Discrete_Random_Variable
s/4.E%3A_Discrete_Random_Variables_(Exercises)
Alcausin, Manikis, Garcia. Fundamentals of
Statistics with applications. Salesiana Publishing Inc.
Page 2-7
Pareño, E.B. and Jimenez, R.O. Basic Statistics. C & E
Publishing Inc. Page 3