Markov Processes for Stochastic Modeling, 2nd Edition

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Basic Concepts in Probability

1.1 Introduction

The concepts of experiments and events are very important in the study of probability. In probability, an experiment is any process of trial and observation. An experiment whose outcome is uncertain before it is performed is called a random experiment. When we perform a random experiment, the collection of possible elementary outcomes is called the sample space of the experiment, which is usually denoted by Ω. We define these outcomes as elementary outcomes because exactly one of the outcomes occurs when the experiment is performed. The elementary outcomes of an experiment are called the sample points of the sample space and are denoted by w_i, i=1, 2, …. If there are n possible outcomes of an experiment, ...