# Accounting and Finance

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SCHOOL OF ECONOMICS, FINANCE AND MANAGEMENT
MSc in Accounting, Finance and Management and
Economics, Finance and Management
ECON 70003

Quantitative Methods
October 2007

Lecture Notes Part 1
Statistics

David Winter
D.Winter@bris.ac.uk

1 Some Basic Concepts
2 Expectations, Moments and Descriptive Statistics
3 Bivariate Distributions
4 Estimation
5 The Normal and Related Distributions and Interval Estimation
6 Hypothesis Testing

These notes provide a summary of the lectures.
They are not a complete account of the unit material.
You should also consult the reading as given in the unit outline and the lectures.

1
10
19
26
35
43

Chapter 1
Some Basic Concepts
1.1 Probability
It is customary to begin courses in statistics with a discussion of probability and then go on to derive certain propositions in probability theory. The problem with this approach is that probability is a difficult and potentially confusing subject. The foundations of probability theory are not well established. There are at least three different ways of thinking about probability.
(a)
(b)
(c)

Relative Frequency
Subjective belief
Mathematical theory

The relative frequency idea of probability is the oldest concept and dates back to the eighteenth century (and probably before) when European mathematicians become interested in analysing games of chance. The basic idea is that the probability of an event occurring is the relative number of times the event occurs in a given number of trials. This introduces the important idea that the probability of the event A occurring lies between 0 and 1, or
0 ≤ P(A) ≤ 1

(1.1)

It also means that the probability of a series of outcomes from a gambling game can be written as a simple sum. This is because these events are mutually exclusive. Thus if there are a series of events A, B, C,….which are...

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