Statistics and Probability grade 11

2. P
R
A
Y
E
R
Oh God, Pour forth your brilliance upon our
dense intellect, dissipate the darkness which
covers us, that of sin and of ignorance. Grant us
a penetrating mind to understand, a retentive
memory, method and ease in learning, the
lucidity to comprehend, and abundant grace in
expressing ourselves. Guide the beginning of
our work, direct its progress, and bring it to
successful completion. This is what we ask
through Jesus Christ, true God and true man,
living and reigning with You and the Father,
forever and ever. Amen.

3. R
E
M
I
N
D
E
R
•Follow the weekly home learning
plan.
•Be guided in our lesson using
your Learning Activity Sheets.
•Make sure to finish the given task
on time and submit it in your
respective barangay.
•Set your priorities and time
management.

4. MELC
The learner illustrates a random variable
(discrete and continuous), distinguishes
between a discrete and a continuous random
variable and finds possible values of a
random variable.
M11/12SP-IIIa-1
M11/12SP-IIIa-2
M11/12SP-IIIa-3

5. RANDOM VARIABLE
Objectives:
Define and illustrate random
variable;
Distinguish between a discrete and a
continuous random variable;
Find the possible values of a random
variable; and
Appreciate random variable in real
life situation.
INTRODUCTION
What I need to know

6. INTRODUCTION
What is new
Answer the following questions.
1. In how many ways can two coins
fall?
2. If three coins are tossed, in how
many ways can it fall?
3. In how many ways can a die fall?
4. In how many ways can two dice
falls?
4
8
6
36

7. Choose the letter of the best answer.
Write the chosen letter on a sheet of
paper.
1. If a coin is tossed, what are the
possible values of the random variable
for the number of heads?
a. 0, 1 c. 1, 2, 3
b. 0, 1, 2 d. 0, 1, 2, 3
DEVELOPMENT
What I know

8. 2. Which of the following is a variable
whose value is obtained by measuring?
a. Continuous c. Interval
b. Discrete d. Nominal
DEVELOPMENT
What I know

9. 3. A variable where the information or data
can take infinitely many values is
a. Quantitative variable
b. Qualitative variable
c. Discrete variable
d. Continuous variable
DEVELOPMENT
What I know

10. 4. Which of the following statement describe a continuous
random variable?
a. The average distance traveled by a jeep in a week.
b. The number of students present in a Class Anthurium.
c. The number of motorcycles owned by a randomly selected
household.
d. The number of girls taller than 5 feet in a random sample
of 10 girls.
DEVELOPMENT
What I know

11. 5. Which of the following is NOT a discrete variable?
a. Number of white marbles in the box
b. Number of students present in the classroom.
c. The weight of a box of soft drinks labeled “8
ounces.”
d. The number of arrivals customers in the
restaurants between 7:00 a. m to 5:00 p.m.
DEVELOPMENT
What I know

12. Correct Answers
1. A
2. A
3. D
4. A
5. C
DEVELOPMENT
What I know

13. Direction: A. Classify the following random variable as discrete or
continuous.
1. A = the number of senators present in the meeting
2. B = the weights in pounds of newly born babies in a hospital
nursery
3. C = the number of ballpens in the box
4. D = the number of students enrolled in Grade 11
in GMATHS
5. E = the height of mango trees in a farm.
DEVELOPMENT
What is in
Activity

14. KNOW MY SAMPLE SPACE
Direction: Complete the table by identifying the sample space of
the given event.
DEVELOPMENT
What is in
Activity
EVENT SAMPLE
SPACE
2 coins are tossed
3 coins are tossed

15. Direction: A. Classify the following random variable as discrete or
continuous.
1. A = the number of senators present in the meeting
2. B = the weights in pounds of newly born babies in a hospital
nursery
3. C = the number of ballpens in the box
4. D = the number of students enrolled in Grade 11
in GMATHS
5. E = the height of mango trees in a farm.
DEVELOPMENT
What is in
Activity and answer
discrete
discrete
discrete
continuous
continuous

16. KNOW MY SAMPLE SPACE
Direction: Each group will complete the table by identifying the
sample space of the given event.
DEVELOPMENT
What is in
Activity and answer
EVENT SAMPLE
SPACE
2 coins are tossed
3 coins are tossed
TH TT
HH HT
HTT HTH
HHH HHT
TTH TTT
THT THH

17. •How do you define random variable?
•How do you classify random variable?
•How do you differentiate discrete from
continuous random variable?
•How do you determine the values
of random variable?
DEVELOPMENT
What is in
Activity-Questions

18. Random Variable
a variable whose
possible values are
determined by chance.
DEVELOPMENT
What is it

19. Classification of Random Variable
Discrete Random Variable – one that
can only take a finite (countable)
number of distinct values.
Continuous Random Variable - can
assume an infinite number of values in
an interval between two specific values.
DEVELOPMENT
What is it

20. DEVELOPMENT
What is it
RANDOM VARIABLES
DISCRETE
A discrete random
variable is a random
variable whose values
represented by count
data. This happens when
the set of possible
outcomes from an
experiment can be
counted such as the
number of household in
a barangay, thus making
the values of the random
variable countable just
like whole numbers 0, 1,
2, 3.
CONTINUOUS
A continuous random
variable is a random
variable that takes
values on a continuous
scale. This happens
when the set of possible
outcomes from an
experiment cannot be
counted but can be
measured such as height
of Grade 11 students.
Continuous random
variables represent
measured data like
height, weight and
temperature.

21. To determine the values of the random
variable,
1. List the sample space of the
experiment.
2. Count the number of the random
variable in each outcome and assign
this number to this outcome.
DEVELOPMENT
What is it

22. Example:
In a box there 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.
1. Determine the sample space. Let
W represent the white ball and Y for
the yellow ball.
2. Count the number of white balls in
each outcome in the sample space
and assign this number to this
outcome.
Solution:
The sample space for this
experiment is:
S = {WW, YY, WY, YW}
So, the possible values of the
random variable X are 0, 1, and 2.
DEVELOPMENT
What is it
Possible Outcomes Value of the random
variable X (Number
of white balls)
WW 2
YY 0
WY 1
YW 1

23. Direction: Classify the following random variable
as discrete or continuous.
1. A = the number of students who joined a field
trip
2. E = the number of gifts received by the birthday
celebrant
3. I = the length of time spent in playing video
games in minutes
4. O = the amount of salt needed to bake a loaf of
bread
5. U = the weight of professional boxers
ENGAGEMENT
What is more
Activity 1 and 2

24. Direction: Answer the following:
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.
1. Complete the table below.
2. What are the values of the random variable D?
ENGAGEMENT
What is more
Activity 1 and 2
Outcomes
Number of Defective Computers
(Value of D)

25. Direction: Classify the following random variable
as discrete or continuous.
1. A = the number of students who joined a field
trip
2. E = the number of gifts received by the birthday
celebrant
3. I = the length of time spent in playing video
games in minutes
4. O = the amount of salt needed to bake a loaf of
bread
5. U = the weight of professional boxers
ENGAGEMENT
What is more
Activity 1 and 2-Answers
Discrete
Discrete
Continuous
Continuous
Continuous

26. Direction: Answer the following:
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.
1. Complete the table below.
2. What are the values of the random variable D? 0, 1, 2, 3
ENGAGEMENT
What is more
Activity 1 and 2-Answers
Outcomes Number of Defective Computers (Value of D)
DDD 3
DDN 2
DND 2
DNN 1
NDD 2
NDN 1
NND 1
NNN 0

27. Trivia: These are cosmic snowballs of frozen gases, rock and dust that orbit the Sun. When frozen, they
are the size of a small town
1. If a die is roll, what are the possible values of the
random variable?
2. A variable whose possible values are determined by
chance.
3. In discrete random variable, finite means
4. If three coins are tossed, how many will be the
sample space?
5. This happens when the set of possible outcomes
from an experiment cannot be counted but can be
measured such as height, weight etc.
6. Suppose you tossed a coin, What are the possible
values of the random variable for the number of
tails?
ASSIMILATION
What I have learned
3 2 1 6 5 4
Directions: Analyze then answer each question and write the matching letter on the rectangle above the
number of its item. In every item there is one corresponding letter that answers the question. (For example:
the answer in number one is M. Therefore, I will write M in the box above the number one.)
C – Countable
E – 0,1
M – 1, 2, 3, 4, 5, 6
O – Random variable
S – Eight 8
T – Continuous
U – 0, 1, 2, 3
M
3 2 1 6 5 4

28. 1. If a die is roll, what are the possible values of the
random variable?
2. A variable whose possible values are determined by
chance.
3. In discrete random variable, finite means
4. If three coins are tossed, how many will be the
sample space?
5. This happens when the set of possible outcomes
from an experiment cannot be counted but can be
measured such as height, weight etc.
6. Suppose you tossed a coin, What are the possible
values of the random variable for the number of
tails?
ASSIMILATION
What I have learned
C – Countable
E – 0,1
M – 1, 2, 3, 4, 5, 6
O – Random variable
S – Eight 8
T – Continuous
U – 0, 1, 2, 3
Trivia: These are cosmic snowballs of frozen gases, rock and dust that
orbit the Sun. When frozen, they are the size of a small town
C O M E T S
3 2 1 6 5 4

29. Direction: Choose the letter of the best
answer. Write your answer on your quiz
notebook.
1. A variable that can be discrete or continuous is
called
A. Random sample
B. Random variable
C. Random notation
D. Random elimination
ASSIMILATION
What I can achieve

30. 2. Which of the following is NOT a discrete variable?
A. Number of books per student
B. Number of green marbles in the box
C. The number of arrivals of customers in the clinic
between 8:00 a. m to 4:00 p.m.
D. The weight of a box of soft drinks labeled 12ounces.
ASSIMILATION
What I can achieve

31. 3. Which of the following is NOT a continuous
random variable?
A. The height of the airplane’s flight
B. The amount of liquid on a container
C. The length of time for the check up in the hospital
D. The number of clients of a certain Insurance
Company each day
ASSIMILATION
What I can achieve

32. For number 4 and 5
Suppose you tossed two coins.
4.What are the sample spaces for the experiment above?
A. HH, TT C. HH, TH, TT
B. HH, HT, TT D. HH, HT, TT, TH
5. What are the possible values of the random variable for
the number of heads?
A.0, 1 C.1, 2, 3
B.0, 1, 2 D.0, 1, 2, 3
ASSIMILATION
What I can achieve

33. Correct Answers