Random Variable (Discrete and Continuous)

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

STATISTICAL
EXPERIMENT
activity
outcome/s
any activity that
produces outcomes

a process that will generate data where the
outcomes have a corresponding chance of
occurrence.
STATISTICAL EXPERIMENT

SAMPLE
SPACE
the set of all possible
outcomes

What is the
sample space?
tossing a die
𝑆 = 1,2,3,4,5,6

What is the
sample space?
tossing two
coins

What is the
sample space?
Tossing a coin
and a die

Drawing a jack from
standard deck of
cards
What is the SAMPLE SPACE?
S={J♠, J♣, J⧫, J♥}

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}

What is the sample
space?
spinning
this wheel

What is the sample
space?
getting a sum
of 7 when a
pair of dice
is tossed

RANDOM
VARIABLE
a variable whose possible
values are determined by
chance

typically represented by an uppercase letter,
usually X, while its corresponding lowercase
letter, x, is used to represent one of its
values
RANDOM VARIABLE

X
Random
Variable
x
Value of a
Random
Variable
RANDOM VARIABLE: Notations

can only take a finite number
of distinct values
DISCRETE RANDOM VARIABLE
countable

can assume an infinite number
of values in an interval between
two specific values.
CONTINUOUS RANDOM VARIABLE
measurable

measurable
countable
infinite
finite
nonnegative
whole
numbers
fractions and
decimals
DISCRETE CONTINUOUS
VS

If the example illustrates a discrete
random variable, type “D”.
If the example illustrates a continuous
random variable, type “C”.
DISCRETE VS CONTINUOUS

5
4
the number of electric fans in
your house
3
DISCRETE or CONTINUOUS
2
1

amount of street food
consumed by Nicholasians per
day
5
4
3
2
1

the number of friends a person
can have
5
4
3
2
1

the number of beautiful
female students in SHS in
San Nicholas III, Bacoor
City, Cavite
5
4
3
2
1

the weight of all male students
in this class
5
4
3
2
1

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

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

Random Variable (Discrete and Continuous)

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