1. Umm Al-Qura University
بسم الله الرحمن الرحيم
Umm Al-Qura University
Health Sciences College at Al-Leith
Department of Public Health
Lecture (5)

2. Random variables

3. Objectives: 1/ Define basics of Random variables.
2/ Define Types of Random variables
3/ Give an Example of Random variables .

4. 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}
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5. Random Variable X = "The score shown on the top face".
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}
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6. 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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7. Cumulative Distribution Function (cdf):
Continuous
Cumulative Distribution Function (cdf):
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8. F(x)=P(X≤x)=∑f(x) Probability distribution function (pdf) : Discrete
Probability Density Function (pdf) :
F(x)=P(X≤x)=∑f(x)
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9. statistic

10. statistic

11. 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 = 1) = 1/6
P(X = 2) = 1/6
P(X = 3) = 1/6
P(X = 4) = 1/6
P(X = 5) = 1/6
P(X = 6) = 1/6
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12. The three coins can land in eight possible ways:
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13. 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
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14. statistic

15. statistic

16. Exercise 9
Two coins are tossed. If Y represents the number of tails, what is P(Y = 1)?
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17. End
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