Date: Sun, 7 Aug 2022 18:37:35 +0000 (UTC) Message-ID: <874118699.5484.1659897455918@localhost> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_5483_1815528969.1659897455917" ------=_Part_5483_1815528969.1659897455917 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Probability theory and statistics

# Probability theory and statistics

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:

## Group 1: The basics

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.

## Group 2: Parameters and sample statistical measures

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.

## Group = 3: Stochastic processes

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:

Bi= nomial process

Poisson process

Hypergeometric process

Central Limit Th= eorem

Renewal processes

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

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