stats

4. .
A random variable is discrete random variable if its
set of possible outcomes is countable. Mostly, discrete
random variables represent count data, such as the
number of defective chairs produced in a factory.
A random variable is a continuous random
variable if it takes values on a continuous scale. Often,
continuous random variables represent measured data,
such as heights, weights, and temperatures.

5. A. Classify the following random variables as
discrete or continuous.
1. The number of defective computers produced by a
manufacturer
2. The weight of newborns each year in a hospital
3. The number of siblings in a family
4. The amount of paint utilized in a building project
5. The number of dropouts in a school
6. The speed of a car
7. The number of female athletes
8. The time needed to finish the test
9. The amount of sugar in a cup of coffee
10. The number of people who are playing lotto each day
11. The number of accidents per year in an accident prone
area
Discrete
Continuous
Discrete
Continuous
Discrete
Continuous
Discrete
Continuous
Continuous
Discrete
Discrete

6. 12. The amount of salt and ice to preserve ice
cream
13. The number of all public school students in the
world
14. The intensity of several earthquakes striking
Mindanao
15. The number of private school teachers in the
Philippines
16. The body temperature of a patient
17. The size of a Flat TV screen
18. The heights of students
19. The number of households in a subdivision
20. The vital statistics a female candidate
21. The number of used clothes for the refugees
22. The number of eggs in one tray
Continuous
Discrete
Continuous
Discrete
Continuous
Continuous
Continuous
Discrete
Continuous
Discrete
Discrete

7. 23. The length of the top of a table
24. The amount of sugar needed to bake
25. The number of students in the TVL track
26. The width of a blackboard
27. The sticks of chalk in a box
28. The coins in my pocket
29. The Korean teachers here at ENHS
30. The kilogram of fruits in a table
31. The storm signals of typhoons
32. The distance between school and market
33. The angle of elevation
34. The height of flagpole
35. The thickness of a book
Continuous
Continuous
Discrete
Continuous
Discrete
Discrete
Discrete
Continuous
Continuous
Continuous
Continuous
Continuous
Continuous
STATISTICS AND PROBABILITY SAMSUDIN N. ABDULLAH,

8. POSSIBLE VALUES OF
RANDOM VARIABLES AND
CONSTRUCTING
PROBABILITY DISTRIBUTION

9. Properties of discrete probability distribution
1. The probability of each value of the random
variable must be between or equal to 0 and 1. In
symbol 0 < P(X) < 1.
2. The sum of all the probabilities of all values of the
random variable must be equal to 1. In symbol, we
write it as ΣP(X) = 1

10. DISCRETE PROBABILITY DISTRIBUTION
A discrete probability distribution is a list of probabilities for
each possible outcome in an experiment. It gives the
probability values of a discrete random variable.
Recall that P(E)= number of favorable outcome
total number of outcomes

11. Example 1. In a box – one red and one blue. Two balls are picked one
at a time with replacement. Let x = be the number of red ball
There are 4 possible outcome.
The information in probability may be presented in form of histogram
Possible Outcomes Number of red balls probability

12. Example:
Write the probability distribution of a random variable Y representing the
number of green balls when 2 balls are drawn in succession without
replacement from a jar containing 4 red and 5 green balls. Construct a
histogram for this probability distribution
Possible Outcomes No. of green balls (y) Probability

13. Example . The resident of a local community were surveyed about the
occupation of each family’s breadwinner. It was found out that 25 of
them are private sector employees, 18 are health care workers 12 are
educators, and 5 if he or she is a government employee
Let x be the number that represents the occupation of a randomly
selected person. That is, let x= 1 if the chosen person is private sector
employee, 2 if he or she health care worker, 3 if he or she is educator
and 4 if he or she a government employee.
a. Create the probability distribution for the random variable x
b. Draw the probability histogram
c. What is the probability that a randomly selected respondent is NOT a
government employee?

14. Activity 1. Work it Up!!!
Identify Whether the given experiments involves a discrete or a continuous
random variable.
1. Rotating a spinner that equally divided into blue,
green, red and yellow section
2. Getting the distance travelled by the car
3. Collecting data about weights of students in a certain
school
4. Tossing a fair of coin 5 times
5. Picking a multiple of 4 less than 1,000,000

15. 6. Checking the monthly expenses of small business
7. Recording the number of turnovers committed by a
basketball team during the games in a season.
8. Tallying the number of gold medals won by the
Philippine in the different Olympic events.
9. The temperature in Cebu at noon time
10. The number of phone calls taken by a call center
agent in a week.

16. .
A total of 20 applicants came in a job interview. Among them,
four were 45 years old, six were 39 years old, three were 42
years old, five were 40 years old, and two were 35 years old.
Let x = age of a randomly selected applicant.
a. Construct the probability distribution for random variable
b. What is the probability that a randomly selected applicant
is 35 years old
c. What is the probability that a randomly selected applicant
is older than 43-years old
d. Draw histogram for the probability distribution.

17. Example 2: Suppose the number 1,2,3, and 6 are
placed on cards, which are place in the box. Two cards
are picked from the box. Let x be the random variable
that gives the product of the two numbers drawn.
a. Construct the probability mass function of x
b. Construct the histogram for probability mass function
(pmf).
c. What is p(x=6)
d. What is p(x ≤ 10 )

18. . Let X be a random variable giving the number of girls in a randomly
selected three-child family. Assuming that boys and girls are equally likely,
construct the probability distribution of X and its corresponding histogram.

19. Mean of Discrete Random Variable
The mean of a probability distribution is given by x
̄ = 𝑥 . 𝑝(𝑥)
Variance of a Discrete Random Variable
Variance is the measure of how spread the data are, so instead of
multiplying each probability with a single data point, it is multiplied by the
sequence of the distance of each data point from the mean.
The variance probability distribution is given by σ2 = 𝑥 − x̄ 2. 𝑝(𝑥).

20. A census taker is gathering data on the gender of the eldest
child in the family. Let x = the number of girls, where x = 1 if
the eldest is a girl and x = 0 otherwise. Find the mean and
variance of the probability distribution for the random variable

21. Example 2. A small study aims to see the correlation between
having a tattoo and cases of clinical depression. In a one group of
12 people from the same age bracket 7 have 1 tattoo, 3 have 2
tattoos and the rest have 3 tattoos. If a person is randomly picked
from this group and evaluated for depression, what is the expected
number of tattoos that the person will have?
Let x be the number of tattoos of a student from the class.

22. Mr. John Cruz, a Mathematics teacher, regularly gives a
formative assessment composed 5 multiple choice items. After
the assessment, he used to check the probability distribution
of the correct responses and the data is presented below: Find
the mean and variance

23. Activity 2: Mean and the
Variance
1. The number of shoes sold per day at a retail store is shown in the
table below. Find the mean, variance, and standard deviation of this
X P(x)
19 0.1
20 0.2
21 0.4
22 0.5
23 0.6

24. The number of inquiries received per day by the Office of
Admission in a certain university is shown below. Find the
variance and the standard deviation.
Number of Inquiries x Probability P(x)
22 0.08
23 0.19
24 0.36
25 0.25
26 0.07
27 0.05