Statistical Inference/Probability Theory: Difference between revisions

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==== Complementation ====
==== Complementation ====


=== Theorem 1.1.4 - Event Operations ===
=== Event Operations [Theorem 1.1.4] ===


== Basics of Probability Theory ==
== Basics of Probability Theory ==

Revision as of 16:40, 26 July 2018

Statistical Inference
Probability Theory
Transformations and Expectations
Common Families of Distributions
Multiple Random Variables
Properties of a Random Sample
Principles of Data Reductions
Point Estimation
Hypothesis Testing
Interval Estimation
Asymptotic Evaluations
Analysis of Variance and Regression
Regression Models

Set Theory

Sample Space [Definition 1.1.1]

The set, S, of all possible outcomes of a particular experiment is called the sample space for the experiment.

Event [Definition 1.1.2]

An event is any collection of possible outcomes of an experiment, that is, any subset of S (including S itself).

Union

Intersection

Complementation

Event Operations [Theorem 1.1.4]

Basics of Probability Theory

Conditional Probability and Independence

Random Variables

Distribution Functions

Density and Mass Functions