Chapter 2.4
Probability Theory

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Overview

An experiment is an action or process that generates observations, and the sample space of an experiment, denoted by S, contains the set of all possible outcomes of that experiment. An event is any collection of outcomes contained in the sample space S.

Axiom

Given an experiment and a sample space S, the objective of probability is to assign to each event A a number P(A), called the probability of the event A.

                         For any event A, P (A ) ≥ 0
                P(S)  =  1                                                       (2.4.1)

                         If A1,A2, ...,Ak is a finite collection of mutually exclusive events, then
     ⋃    ⋃    ⋃         ∑k
P(A1   A2   ...  Ak)  =      P(Ai)                                               (2.4.2)
                          i=1
                         If A1,A2, A3,... is a infinite collection of mutually exclusive events, then
     ⋃    ⋃    ⋃         ∑∞
P(A1   A2   Ak   ...)  =      P(Ai)                                               (2.4.3)
                          i=1
                                                                                 (2.4.4)