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Stat1801
Probability and Statistics: Foundations of Actuarial Science
Fall 20102011
Chapter I
Probability
§ 1.1
Introduction
Presence of uncertainty :
•
An investor chooses between buying stocks and tying up assets in real estate in
an uncertain economic period.
•
A college student decides how much time should be spent studying for a
midterm exam.
•
A gambler decides what option he should put his bet on.
•
An offspring may or may not inherit a specific genetic disease from the parents.
Probability
•
Objective and quantitative assessment of how certain (or how likely) an event
will occur.
•
Basic tool in statistical inference.
Example
Probability Theory
Statistical Inference
_
1.
We have a fair coin
.
W
e
h
a
v
e
a
c
o
i
n
.
(i.e.
()
( )
5
.
0
=
=
T
P
H
P
)
2.
The fair coin is tossed ten times.
This coin is tossed ten times.
3.
P
(all are head) = ?
All are head.
4
.
I
s
i
t
a
f
a
i
r
c
o
i
n
?
From probability theory, if the coin is fair, then
P
(all are head) =
.
10
5
.
0
If it is a fair coin, it is very unlikely for us to observe ten heads in a row. So for
statistical inference, we may reach a conclusion that the coin is not a fair coin.
p.1
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Probability and Statistics: Foundations of Actuarial Science
Fall 20102011
§ 1.1.1
Probability
in Engineering and the Sciences
Quantify the uncertainty in measurements
•
Imprecise instruments and human error can result in recorded observations
that are different from the true values.
•
The quantity being measured can be in flux (i.e. continually changing) with
the result that the recorded observation need not be descriptive of the
quantity in the future, e.g. voltage in an alternating current electric circuit.
Quality control
•
Maintenance of quality in manufacturing processes.
•
Minimize the number of defects produced by a manufacturing process under
reasonable costs.
•
Identify defects before they leave the production line, by inspection on a
sample
of items and then making inferences about the number of defectives
produced in total.
•
Probability can be used to analyse the uncertainty in these inferences and to
determine the size of the sample to be tested.
Reliability
•
Concerned with lifetimes of electrical and mechanical systems.
•
Probability can be used to analyse the uncertain lifetimes of such systems
and to assist the engineer in designing systems that are both reliable and cost
effective.
Queuing
•
Analysis and design of systems involving multiple servers and clients, e.g.
computer networks, service line at a bank or post office.
•
Probability can be used to analyse the uncertain waiting and service times in
such queues and to assist the engineer or computer scientist in designing a
system that meets the demands imposed on it in the most costeffective way.
p.2
Stat1801
Probability and Statistics: Foundations of Actuarial Science
Fall 20102011
§ 1.1.2
Probability
in Financial Engineering
Risk management
•
Analyse risk in financial markets and design products (investment strategies,
portfolio) and techniques to manage that risk.
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This note was uploaded on 02/01/2012 for the course STAT 1801 taught by Professor Mrchung during the Fall '10 term at HKU.
 Fall '10
 MrChung
 Statistics, Probability

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