The document outlines a statistics and probability course, emphasizing the understanding of random variables, sampling techniques, hypothesis testing, and data analysis. It introduces two types of random variables: discrete, which assumes countable values, and continuous, which can take any value within an interval. Various examples and assessments guide students in classifying different types of variables.

1. STATISTICS &
PROBABILITY

2. COURSE DESCRIPTION
At the end of the course, the
students must know how to find
the mean and variance of a
random variable, to apply sampling
techniques and distributions,
to estimate population mean and
proportion, to perform hypothesis
testing on population mean and
proportion, and to perform
correlation and regression

3. PERFORMANCE TASK
… to conduct a survey and
analyze the result using
statistics

4. LESSON 1
Random
Variables &
Its
Probability

5. A. VARIABLES
A variable is a
characteristic or
condition that can
change or take on
different values.

6. RANDOM
VARIABLES
1. Random Variable (RV): A
numeric outcome that
results from an experiment
2. For each element of an
experiment’s sample space,
the random variable can
take on exactly one value

7. RANDOM
VARIABLES
3. Random Variables are
denoted by upper case
letters (Y)
4. A random variable assumes
numerical values associated
with the random outcome of an

8. TYPES OF RANDOM
VARIABLES
1. A discrete random
variable can assume a
countable number of values.
Number of steps to the top of the
Eiffel Tower

9. Discrete variables are
countable in a finite amount of
time. For example, you can
count the change in your
pocket. You can count the
money in your bank account.
You could also count the
amount of money
in everyone’s bank account. It
might take you a long time to
count that last item, but the

10. Discrete Random Variables
Number of sales
Number of calls
Shares of stock
People in line
Mistakes per page
Variables that can only
take on a finite number of
values

11. © 2011 Pearson Education, Inc
Discrete Random Variable Examples
Experiment Random
Variable
Possible
Values
Count Cars at Toll
Between 11:00 & 1:00
# Cars
Arriving
0, 1,
2, ..., ∞
Make 100 Sales Calls
# Sales 0, 1, 2, ..., 100
Inspect 70 Radios # Defective
0, 1, 2, ..., 70
Answer 33 Questions
# Correct0, 1, 2, ..., 33

12. TYPES OF RANDOM
VARIABLES
2. A continuous random
variable can assume any value
along a given interval of a number
line.
The time a tourist stays at the top
once he gets there

13. • Continuous Random
Variables
–Length
–Depth
–Volume
–Time
–Weight
Variables that can take on
an infinite number of
possible values

14. © 2011 Pearson Education, Inc
Continuous Random Variable
Examples
Measure Time
Between Arrivals
Inter-Arrival
Time
0, 1.3, 2.78, ...
Experiment Random
Variable
Possible
Values
Weigh 100 People Weight 45.1, 78, ...
Measure Part Life Hours 900, 875.9, ...
Amount spent on food$ amount 54.12, 42, ...

15. Formative Assessment
Classify the following
according to type of
variable.

16. 1. The number of goods
sold in a retail store
2. Volume of gasoline
consumed by an
automatic car
3. Names listed in a voting
center
4. Outcomes when tossing
a coin

17. 6. Diastolic blood pressure
7. Thickness of a book
8. Intensity of earthquake
9. The components of
vectors
10. Color of hair

18. Activity 3.1 – A
Identify if the given
information/condition is a
Continuous or Discrete
Variable

19. 1. Amount of sugar intake
in a day
2. Number of SUV along
EDSA during rush hour
3. Number of students
present during the
Christmas Party
celebration
4. Average height of Grade

20. 5. The number of home
runs in a baseball game
6. Final score in a Quarterly
Assessment
7. Distance in meters of JHS
and SHS buildings.

21. 8. Gender of a new born
baby
9. Body temperature
10. Speed of a motorcycle