Learning Competencies - to recall statistical experiment and sample space - to illustrate a random variable (discrete and continuous). - to distinguish between a discrete and a continuous random variable.

1. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
RandomVariable:
Discrete & Continuous
Statistics and Probability
PRINCESS P. DIPASUPIL
Special ScienceTeacher I

2. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
STATISTICAL
EXPERIMENT
activity
outcome/s
any activity that
produces outcomes

3. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
a process that will generate data where the
outcomes have a corresponding chance of
occurrence.
STATISTICAL EXPERIMENT

4. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
SAMPLE
SPACE
the set of all possible
outcomes

5. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
What is the
sample space?
tossing a die
𝑆 = 1,2,3,4,5,6

6. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
What is the
sample space?
tossing two
coins

7. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
What is the
sample space?
Tossing a coin
and a die

8. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
Drawing a jack from
standard deck of
cards
What is the SAMPLE SPACE?
S={J♠, J♣, J⧫, J♥}

9. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
What is the sample
space?
tossing a
pair of dice
S={ 11 21 31 41 51 61
12 22 32 42 52 62
13 23 33 43 53 63
14 24 34 44 54 64
15 25 35 45 55 65
16 26 36 46 56 66}

10. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
What is the sample
space?
spinning
this wheel

11. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
What is the sample
space?
getting a sum
of 7 when a
pair of dice
is tossed

12. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
RANDOM
VARIABLE
a variable whose possible
values are determined by
chance

13. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
typically represented by an uppercase letter,
usually X, while its corresponding lowercase
letter, x, is used to represent one of its
values
RANDOM VARIABLE

14. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
X
Random
Variable
x
Value of a
Random
Variable
RANDOM VARIABLE: Notations

15. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
can only take a finite number
of distinct values
DISCRETE RANDOM VARIABLE
countable

16. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
can assume an infinite number
of values in an interval between
two specific values.
CONTINUOUS RANDOM VARIABLE
measurable

17. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
measurable
countable
infinite
finite
nonnegative
whole
numbers
fractions and
decimals
DISCRETE CONTINUOUS
VS

18. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
If the example illustrates a discrete
random variable, type “D”.
If the example illustrates a continuous
random variable, type “C”.
DISCRETE VS CONTINUOUS

19. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
5
4
the number of electric fans in
your house
3
DISCRETE or CONTINUOUS
2
1

20. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
amount of street food
consumed by Nicholasians per
day
DISCRETE or CONTINUOUS
5
4
3
2
1

21. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
the number of friends a person
can have
DISCRETE or CONTINUOUS
5
4
3
2
1

22. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
the number of beautiful
female students in SHS in
San Nicholas III, Bacoor
City, Cavite
DISCRETE or CONTINUOUS
5
4
3
2
1

23. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
the weight of all male students
in this class
DISCRETE or CONTINUOUS
5
4
3
2
1

24. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
Determine whether the random variable X orY is
discrete or continuous.
1. X = number of players in a randomly selected PBA team
2.Y = the height in inches of a randomly selected person
inside the coffee shop
3. X = the number of things in your personal collection
4.Y = the number of COVID-19 tests done in a randomly
selected day
5. X = the amount in pesos of fund allegedly stolen by
former officials of a randomly selected government agency

25. Statistics and Probability • PRINCESS P. DIPASUPIL
• Special ScienceTeacher I
Determine whether the random variable X orY is
discrete or continuous.
1. X = number of players in a randomly selected PBA
team
2.Y = the height in inches of a randomly selected
person inside the coffee shop
3. X = the number of things in your personal collection
4.Y = the number of COVID-19 tests done in a
randomly selected day
5. X = the amount in pesos of fund allegedly stolen by
former officials of a randomly selected government
agency
• discrete
• continuous
• discrete
• discrete
• continuous