This set of topics gathers together the essentials of probability theory= that you need to know as a risk analyst. The topics are split into three g= roups:

We start by offering a discussion of the meaning of probability. It's surprising how much we take this idea fo= r granted, and an appreciation of different viewpoints will help you disent= angle probability and uncertainty.

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

The section on probability para= meters explains the meaning of standard statistics like mean and varian= ce within the context of probability distributions. That comparison of the = meaning of these statistics for uncertainty and frequency distributions is = discussed elsewhere.

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

The section on probability theore= ms explains some fundamental probability theorems most often used in mo= deling risk, and some other mathematical concepts that help us manipulate a= nd explore probabilistic problems.

There are five different circumstances in which we use descriptive param= eters to describe distributions:

Frequency distributions of populations

Frequency distributions of samples

Probability distributions of random varia= bles

Uncertainty distributions of real-world p= arameters

Frequency distributions of Monte Carlo si= mulation results

The calculation and interpretation of the = statistical measures will depend on which of these five distributions you a= re describing.

Stochastic processes are types of random behavior, and the mathematical = descriptions of these types of behavior are the building blocks of probabil= ity modeling and statistics. That means you really need to know them!

We describe the following processes:

There are a number of other stochastic pro= cesses, essentially variations of the above, that are used in modeling time= series.