RANDOM
VARIABLES
HELLO DEAR
STUDENTS
In this lesson, the concept of a random variable is discussed. The notion of a
statistical experiment is defined as well as random variables that relate to
experiments. Finally, two types of random variables, discrete and continuous,
are described.
AFTER THIS
LESSON,
YOU
SHOULD BE
ABLE TO:
ILLUSTRATE/PROVIDE EXAMPLES OF
RANDOM VARIABLES
DISTINGUISH BETWEEN DISCRETE AND
CONTINUOUS RANDOM VARIABLE
FIND THE POSSIBLE VALUES OF A RANDOM
VARIABLE
ACTIVITY
1. Toss a coin three times
and record the results of
the three tosses below.
(Use H for heads and T
for tails.)
OUTCOME
FIRST TOSS
2. Count the number of
heads that appeared.
3. Write all possible
outcomes for tossing a
coin three times, and
then count the number of
heads for each outcome.
List them down.
SECOND TOSS
THIRD TOSS
ACTIVITY
Hold your
breath and
accurately
record the time
you held your
breath.
(If possible, use a cell
phone timer and record
up to the nearest
hundredth of a second).
Record the time below:
________ seconds
STATISTICAL
EXPERIMENT
An activity that will produce outcomes, or a
process that will generate data. The outcomes
have a corresponding chance of occurrence.
STATISTICAL
EXPERIMENTS
Statistical Experiments can have a
few or a lot of possible outcomes.
Numb
e
l
HEAD
er
ho
s
W
G A CO
N
I
S
S
IN
O
T
TAIL
Natural
Numbers
YEAR OF BIRTH
1980
1985
1978
1981
1937
1990
1976
Random Variable
X Outcome
Number
RANDOM VARIABLE
a way to map outcomes of a
statistical experiment
determined by chance into
number
1
=
d
a
He
2
Tail = 2
"Complex
Number."Britannica,https://www.britannica.com/science/complexnumber. Accessed 10 Oct 2021
TYPES OF RANDOM
VARIABLE
- DISCRETE RANDOM VARIABLE
-CONTINUOUS RANDOM VARIABLE
DISCRETE
RANDOM
VARIABLE
THE NUMBER OF
HEADS WHEN
TOSSING A COIN
TWICE
are random variables that can take on a
finite (or countably infinite) number of
distinct values.
NUMBER OF
STUDENTS
PRESENT IN A
CLASSROOM
CONTINUOUS
RANDOM
VARIABLE
are random variables that take an
infinitely uncountable number of possible
values, typically measurable quantities.
the time a
person can
hold his/her
breath,
ct
a
x
e
the
f
o
t
h
weig
s
l
a
m
i
n
a
e
th
o
o
z
in the
the t
ime i
t
take
s for
a
pers
on to
bath
e
GROUP
ACTIVITY
Given the following
experiments and random
variables, identify what the
possible values of the
random variables are. Also,
for each random variable,
identify whether the variable
is discrete or continuous.
1. Roll a pair of dice
2. Ask a friend about preparing for a quiz
in statistics
3. Record the sex of family members in a
family with four children
4. Buy an egg from the grocery
5. Record the number of hours one
watches TV from 7 pm to 11 pm for the
past five nights.
GROUP
ACTIVITY
Given the following
experiments and random
variables, identify what the
possible values of the
random variables are. Also,
for each random variable,
identify whether the variable
is discrete or continuous.
1. Experiment: Roll a pair of dice
Random Variable: Sum of numbers that appears in
the pair of dice
2. Experiment: Ask a friend about preparing for a quiz
in statistics
Random Variable: How much time (in hours) he/she
spends studying for this quiz
3. Experiment: Record the sex of family members in a
family with four children Random Variable: The
number of girls among the children
4. Experiment: Buy an egg from the grocery Random
Variable: The weight of the egg in grams
5. Experiment: Record the number of hours one
watches TV from 7 pm to 11 pm for the past five
nights.
Random Variable: The number of hours spent
watching TV from 7 pm to 11 pm
THANK
YOU!
READ MORE ABOUT RANDOM
VARIABLES HERE:
HTTPS://WWW.KHANACADEMY.ORG/MATH
/STATISTICS-PROBABILITY/RANDOMVARIABLES-STATS-LIBRARY/RANDOMVARIABLES-DISCRETE/V/DISCRETEPROBABILITY-DISTRIBUTION