The basics of probability theory

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See also: Probability theory and statistics introduction, Stochastic processes introduction, Parameters and sample statistics introduction

We define some basic statistics in common use. We look at a few probability concepts that are essential to understand if one is to be assured of producing logical models.

Note that this section is designed to offer a reference of statistical and probability concepts. The application of these principles is left to the appropriate section elsewhere in this help file.

Probability rules and Venn diagrams

The section on probability rules and diagrams explains visual ways to depict probability ideas, and rules for the manipulation of probabilities in calculations.

1. • Definition of probability

   • Probability event notation

   • Basic probability manipulation

   • Conditional probability

   • Venn diagrams

   • Event trees

   • Fault trees

Probability distribution equations

The section on probability equations explains the equations that define probability distributions: pmf, pdf, cdf.

1. • Cumulative distribution function F(x) (cdf)

   • Probability mass function f(x) or p(x) (pmf)

   • Probability density function f(x) (pdf)

Descriptive parameters for probability distributions

The section on probability parameters explains the meaning of standard statistics like mean and variance within the context of probability distributions. That comparison of the meaning of these statistics for uncertainty and frequency distributions is discussed elsewhere.

1. • Location:      Mode, Median, Mean

   • Spread:        Standard deviation, Variance

   • Shape:         Skewness, Kurtosis

Probability theorems

The section on probability theorems explains some fundamental probability theorems most often used in modeling risk, and some other mathematical concepts that help us manipulate and explore probabilistic problems.

1. • The Strong law of Large Numbers

   • Central Limit Theorem (CLT)

   • Binomial Theorem

   • Bayes Theorem

Modeling techniques

1. • Tchebysheffs Rule (or Theorem)

   • Least Squares Regression

   • Rank Order Correlation

   • Taylor and Maclaurin Series Expansion

Read on: Probability rules and diagrams introduction

© Vose Software™ 2007. Reference Number: M-M0915-A