The document explains the concept of random variables, including definitions and distinctions between discrete and continuous random variables. It provides examples of random variables and demonstrates how they can be represented numerically in relation to various chance events. Key concepts include possible outcomes, measures of probability, and the notation used for random variables.

1. RANDOM
VARIABLE

2. 3
OBJECTIVES:
2
4
Illustrates a random variable,
finds the possible values of a
random variable.
distinguishes between a discrete
and a continuous random variable,
1 Define random variable

3. Review
1)
2)
Aside from decimal , probability
may be expressed as these two.
3)The possible outcomes of an
experiment.
4)Set of possible outcomes of an
experiment.
5)Tells how often a certain event will
happen.
FRACTION
PERCENTAGE
EVENT
SAMPLE SPACE
PROBABILITY

4. RANDOM VARIABLE
 Is a variable that assumes numerical values associated with
the random outcomes of an experiment, where one (and
only one) numerical value is assigned to each sample point.
 Is the result of a chance event, that you can measure or
count.
 We use uppercase letter to denote random variables.
Examples:
𝑿 =
𝟏 𝒊𝒇 𝒊𝒕 𝒓𝒂𝒊𝒏𝒔
𝟎 𝒊𝒇 𝒏𝒐 𝒓𝒂𝒊𝒏
𝒀 = 𝒊𝒏𝒕𝒆𝒈𝒆𝒓𝒔 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝟎 𝒂𝒏𝒅 𝟓
𝒀 = {𝟏, 𝟐, 𝟑, 𝟒}
𝒁 = 𝒘𝒆𝒊𝒈𝒉𝒕 𝒊𝒏 𝒌𝒈 𝒐𝒇 𝒂 𝒏𝒆𝒘 𝒃𝒐𝒓𝒏 𝒃𝒂𝒃𝒚 𝒁 = 𝟐. 𝟓 ≤ 𝒛 ≤ 𝟒. 𝟓
𝑿 = {𝟎, 𝟏}

5. Guess me right!
Discrete Continuous
Mistakes per
page
The thickness of a
book
The number of
bottled water in a
box
People queuing
Your height
The depth of water
in the ocean
Number of words
in an essay
Discrete- can assume a countable number of values.
Continuous- have an infinite continuum of possible values.

6. ODD ONE OUT
Number of
push ups you
can do in five
minutes
Let’s Exercise
Number of
days in a
week you
exercise
Amount of
calories
burned after
an exercise
Number of
steps for a
15-minute
walk

7. ODD ONE OUT
How fast can
a sneeze
spread
germs?
Science Matters
How long does
the virus that
causes COVID-
19 last on
surfaces?
Stay at least 1
meter distance
to avoid contact
with droplets
Number of
ways a virus
may be
transmitted

8. Time before
you received
an email from
your colleague
ICT Version
Distance
reached by Wi-
Fi connection
Length of cable
from the server
to working
station
Number of
e-mails sent
in a day
ODD ONE OUT

9. ODD ONE OUT
The volume of
gasoline in a
Honda Beat
Motorcycle.
Road Trip
The number of
motorists that
gas up today.
The distance
travelled with a
full tank
motorcycle.
The length of
time between
motorists in a
gasoline station
ODD ONE OUT

10. ODD ONE OUT
I am 150 cm
tall.
Me, Myself, and I
I weigh 56
kilograms.
I have two
wonderful
sons.
My foot
measures 9
inches.
ODD ONE OUT

11. POSSIBLE VALUES OF RANDOM VARIABLE
1. Tossing a coin. Name the random
variable T.
𝑇 =
0 𝑖𝑓 𝑕𝑒𝑎𝑑
1 𝑖𝑓 𝑡𝑎𝑖𝑙 𝑇 = {0,1}
2. Rolling a die.
𝐷 = 𝑡𝑕𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑠𝑕𝑜𝑤𝑛 𝑜𝑛 𝑡𝑕𝑒 𝑡𝑜𝑝 𝑓𝑎𝑐𝑒
𝐷 = {1,2,3,4,5,6}

12. POSSIBLE VALUES OF RANDOM VARIABLE
3. Couple plans to have 3 children.
𝐺 = 𝑡𝑕𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑔𝑖𝑟𝑙𝑠 𝑡𝑕𝑒 𝑐𝑜𝑢𝑝𝑙𝑒 𝑚𝑎𝑦 𝑕𝑎𝑣𝑒
BBB
BBG
BGB
BGG
GBB
GBG
GGB
GGG
0
1
1
2
1
2
2
3
𝑮 = {𝟎, 𝟏, 𝟐, 𝟑}
B
G
B
G
B
G
G
G
G
B
B
B
BBB
BBG
BGB
BGG
GBB
GBG
GGB
GGG
B
G