Probability and Agency: Introduction

Introduction to Probability Theory

In probability theory, we are given a set Ω of outcomes ω, and try to consider the probabilities of subsets A ⊂ Ω, which we call events. To this end, we define a probability measure Pr(·) or μ(·) (we will use each notation interchangably) that is a function from these sets A ⊂ Ω → [0, 1]. As a technical complicate, μ or Pr may only be defined on some of the subsets of Ω, but this will be adress...

Introduction to Probability

The rule of sum says that the number of ways to choose an element from one of two disjoints sets is the sum of the cardinalities of the sets. That is, if A and B are two finite sets with no members in common, then |A ∪B| = |A|+ |B|. The rule of product says that the number of ways to choose an ordered pair is the number of ways to choose the first element from A and the second element from B. T...

Introduction to Probability

Introduction to Probability

Introduction to Probability

To our wives and in memory of Reese T. Prosser ii Preface Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Format solved continued to influence such early researchers as Huygens, Bernoulli, and DeMoivre in establishing a mathemat...