This presentation helps the students to find the possible values of a random variable. M11/12SP-IIIa-3 and llustrate a probability distribution for a discrete random variable and its properties.

1. 3rd Quarter
Statistics and
Probability

2. Mutual respect
Equality
Active participation
Nonjudgmental attitude
Follow

4. INSTRUCTIONS:
•The students will have a race in getting the ball.
•The teacher will randomly pause or stop the
music at any point during the song.
•When the music stops, the student who is not
holding the ball must answer a question

5. Direction: Classify each random
variable as discrete or
continuous.
• 1. The number of coins that match when
three coins are tossed at once.

6. Direction: Classify each random
variable as discrete or
continuous.
• 2. The number of games in the next World
Cup Series (best of four up to seven games).

7. Direction: Classify each random
variable as discrete or
continuous.
• 3. The amount of liquid in a 12-ounce can of
soft drink.

8. Direction: Classify each random
variable as discrete or
continuous.
• 4. The average weight of newborn babies
born in the Philippines in a month.

9. Direction: Classify each random
variable as discrete or
continuous.
• 5. The number of heads in two tosses of coin.

10. FLOWER QUEST:
GROUP CHALLENGE

11. INSTRUCTIONS:
1. Divide the class into six groups.
2. Give each group a flower with a hidden task to
solve.
3. After solving it, one member gets a secret
question from the teacher.
4. Answering the question earns the group 5 points.

12. QUESTIONS:
• a. What do you call to the value
that we got from our activity?
• b. How do you define mean?

13. Module 2:
Solving Problems Involving
Mean
of Probability Distributions

14. OBJECTIVES:
At the end of the lesson, the students are expected
to:
a. discuss the definition and formula for the value
of mean;
b. calculate the mean of a discrete random variable
using real-life problems; and
c. interpret the result of the mean of a discrete
random variable.

15. Mean of
Discrete
Random
Variable
01.

16. Mean of Discrete
Random Variable
• The mean of a discrete random variable X is also
called the expected value of X.
• The discrete random variable X assumes values
or outcomes in every trial of an experiment with
their corresponding probabilities.

17. Mean of Discrete
Random Variable
• The expected value of X is denoted by
E (X) or μ

18. Mean of Discrete
Random Variable
• • We can get the mean or expected value of the
probability distribution by getting the sum of the
values under the third column.
• We use the formula:
E(x) = [ x . P(x) ]
∑

19. • A researcher surveyed the
households in a small town. The
random variable X represents
the number of college
graduates in the households.
The probability distribution of X
is shown on the right. Find the
expected value of the number
of college graudates in the
households

20. Example 2.
Grade 11 students were asked to estimate the
length (in inches) of a table. The error in the
estimated values were recorded and
tabulated as follows:

21. Example 2.
E(x) = [ x . P(x) ]
∑
= [ (2) ( 0.25) + (3) (0.10) + (4) (0.30) + (5) (0.15) + (6) (0.20) ]
=( 0.5 + 0.3 + 1.2 + 0.75 + 1.2 )
= 3.95 is the average error in the estimated values that were
recorded

22. • In Grade 11 ICT 4 students , the PE teacher is studying the
Body Mass Index (BMI) of students to understand their
health profiles better. The teacher categorizes the BMI into
four distinct groups with the following probabilities:
• 1. Underweight (less than 18.5): Probability = 0.30
• 2. Normal Weight (between 18.5 and 24.9) : Probability= 0.54
• 3. Over Weight ( between 25 and 29.9): Probability= 0.09
• 4. Obesity (greater than 30): Probability= 0.07

23. • The teacher wants to calculate the Mean category of BMI
among students using the probabilities. For calculation
purposes, the teacher assign the categories numerical
values, such as:
Underweight = 1 Normal Weight = 2
Over Weight =3 Obesity =4

24. Follow-up Questions:
• 1. If you are underweight, how will you
improve your nutritional status?
• 2. If you have a normal BMI, how will
you maintain your nutritional status?

25. “Preserve and Conserve:
Unveiling the World of
Crocodile
in the Philippines”

26. REVIEW

27. • 1. The numerical quantity that is assigned to
the outcome of an experiment is called .
• a. sample space
• b. variable
• c. sample
• d. random Variable

28. • 2. The one that can assume only a countable
number of values is known as.
• a. continuous random variable
• b. discrete random variable
• c. sample Space
• d. random Variable

29. • 3. The random variable that can assume an
infinite number of values in one or more
intervals is called .
• a. continuous random variable
• b. discrete random variable
• c. sample Space
• d. random Variable

30. • 4. The discrete random variable is generated
from an experiment in which things are
counted but not measured.
• a. True
• b. False
• c. Neither
• d. Either

31. • 5. The following statements are examples of discrete
random variable, except,
• a. the number of senators present in the franchise
hearing
• b. the number of chalks in the box
• c. the number of frontliners who are positive of
COVID-19
• d. the length of wire ropes

32. • 6. The following statements are examples of
continuous random variable, except,
• a. the area of lots in a subdivision
• b. the time it takes the virus stay on surfaces
• c. the number of learners who joined the online class
• d. the weight of newborn babies for the month of
May

33. • 7. The correspondence that assigns
probabilities to the values of a random
variable.
• a. Probability Distribution
• b. Random Variable
• c. Continuous Random Variable
• d. Discrete Random Variable

34. • 8. It is a graph that displays the possible values of
discrete random variable on the horizontal axis and
the probabilities of those values on the vertical axis.
• a. Bar graph
• b. Line Graph
• c. Pie Chart
• d. Probability histogram

35. • 9. It associates to any given number the probability
that the random variable will be equal to that
number.
• a. Probability Mass Function
• b. Probability histogram
• c. Continuous Random Variable
• d. Discrete Random Variable

36. • 10. The set of all possible outcomes of an
experiment.
• a. Sample space
• b. Variable
• c. Sample
• d. Random Variable

37. • 10. The set of all possible outcomes of an
experiment.
• a. Sample space
• b. Variable
• c. Sample
• d. Random Variable

38. Activity 1. The table below shows the values of ripe mangoes and
the number of occurrences of each value of the random variable.
Determine the probability of the following values of the random
variable R.

39. Find the expected value or the mean of probability distribution.

40. Find the expected value or the mean of probability distribution.

41. Activity 2: Two balls are drawn in succession
without replacement from a jar containing 4
green balls and 3 orange balls. What is the
probability distribution for the number of
green balls? Then, solve for the mean, variance,
and the standard deviation of the probability
distribution.

42. Solution:
List the sample space of this experiment. Let G be a
random variable whose values are the possible number
of green balls that can be drawn from a jar. Then, we let
O be a random variable whose values are the possible
number of orange balls that can be drawn from a jar.
S = {GG, GO, OG, OO}

43. Since, we are looking for the probability of the random
variable G, we need to identify the number of G in each
outcome. So, we have,

44. Or
0.25
Or
0.50
Or
0.20

45. Therefore, the probability distribution of the random variable
G can be written as follows:

46. What is the value of the Mean?
Or
0.25
Or
0.50
Or
0.25

47. What is the value of the Mean?
Or
0.25
Or
0.50
Or
0.25
Or
0.50
Or
0.50
1

48. What is the value of the Variance?

49. What is the value of the Variance?
We use the formula:
Ơ^2=Σ[G^2• P(G)] – μ^2
Or
0.50
Or
0.50
Or
0.50

50. Or
0.50
Or
0.50
Or
0.50

51. What is the value of the standard deviation?

52. Activity: Find the mean, variance, and standard
deviation of the given probability distribution
below. ( 1 whole sheet of paper)