‫بسم هللا الرحمن الرحيم‬
Umm Al-Qura University
Health Sciences College at Al-Leith
Department of Public Health
Lecture (5)
Random variables 
Objectives:
1/ Define basics of Random variables.
2/ Define Types of Random variables
3/ Give an Example of Random variables .
A Random Variable is a set of possible values from 
a random experiment.
Tossing a coin: we could get Heads or Tails.
Let's give them the


values Heads=0 and Tails=1 and we have a Random
Variable "X":
X = {0, 1}
statistic

4
Throw a die once
Random Variable X = "The score shown on the top face".
X could be 1, 2, 3, 4, 5 or 6
So the Sample Space is {1, 2, 3, 4, 5, 6}
statistic
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Types of Random Variables

Discrete: Takes integer values

Binary: Will an individual default (X=1) or not (X=0)?

How many messages arrive at a switch (customers at a service point) per unit of time?

Finite: How many female children in families with 4 children; values = 0,1,2,3,4?

Infinite: How many people will catch a certain disease per year in a given population?
Values = 0,1,2,3,… (How can the number be infinite? It is a model.)

Continuous: A measurement.

How long will a light bulb last? Values X = 0 to ∞

Performance of financial assets over time

How do we describe the distribution of biological measurements?

Measures of intellectual performance
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Continuous
Cumulative Distribution Function (cdf):
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Discrete
Probability distribution function (pdf) :
Probability Density Function (pdf) :
F(x)=P(X≤x)=∑f(x)
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P(X = value) = probability of that value
Throw a die once
X = {1, 2, 3, 4, 5, 6}
In this case they are all equally likely, so the probability
of any one is 1/6
P(X
P(X
P(X
P(X
P(X
P(X
=
=
=
=
=
=
1)
2)
3)
4)
5)
6)
=
=
=
=
=
=
1/6
1/6
1/6
1/6
1/6
1/6
statistic
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The three coins can land in eight possible ways:
X = "number
of Heads"
HHH
3
HHT
2
HTH
2
HTT
1
THH
2
THT
1
TTH
1
TTT
0
statistic
5
Two dice are tossed
The Random Variable is X = "The sum of the scores on the two dice".
Let's make a table of all possible values
1st Die
1 2 3 4 5 6
1 2 3 4 5 6 7
2nd
Die 2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
statistic
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14
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15
Two coins are tossed.
If Y represents the number of tails, what is P(Y = 1)?
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