A Course in Statistics with R

Chapter 5Probability Theory

Package(s): prob, scatterplot3d, ConvergenceConcepts

5.1 Introduction

Probability is that arm of science which deals with the understanding of uncertainty from a mathematical perspective. The foundations of probability are about three centuries old and can be traced back to the works of Laplace, Bernoulli, et al. However, the formal acceptance of probability as a legitimate science stream is just a century old. Kolmogorov (1933) firmly laid the foundations of probability in a pure mathematical framework.

An experiment, deterministic as well as random, results in some kind of outcome. The collection of all possible outcomes is generally called the sample space or the universal space. An example of the universal space of a deterministic experiment is the distance traveled as a consequence of the application of some force is . On the other hand, for a random experiment of tossing a coin, the sample space consists of the set {Head, Tail}. The difference between these two types of experiments is the result of the final outcome. For a stationary object, if the application of a force results in an acceleration of , the distance traveled after 60 seconds is known by the formula . That is, given the acceleration and time, the distance is uniquely determined. ...