Notes on Probability Theory and Statistics

Notes on Probability Theory and Statistics

Antonis Demos (Athens University of Economics and Business)

October 2002

2

Part I Probability Theory

3

Chapter 1

INTRODUCTION

1.1 Set Theory Digression

A set is defined as any collection of objects, which are called points or elements. The biggest possible collection of points under consideration is called the space, universe, or universal set. For Probability Theory the space is called the sample space.

A set A is called a subset of B (we write A B or B A) if every element of A is also an element of B. A is called a proper subset of B (we write A B or B A) if every element of A is also an element of B and there is at least one element of B which does not belong to A.

Two sets A and B are called equivalent sets or equal sets (we write A = B) if A B and B A.

If a set has no points, it will be called the empty or null set and denoted by .

The complement of a set A with respect to the space , denoted by A?, Ac, or - A, is the set of all points that are in but not in A.

The intersection of two sets A and B is a set that consists of the common elements of the two sets and it is denoted by A B or AB.

The union of two sets A and B is a set that consists of all points that are in A or B or both (but only once) and it is denoted by A B.

The set difference of two sets A and B is a set that consists of all points in

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download