Statistical Inference/Probability Theory: Difference between revisions

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== Set Theory ==
== Set Theory ==


=== Definition 1.1.1 - Sample Space ===
=== 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.
The set, ''S'', of all possible outcomes of a particular experiment is called the ''sample space'' for the experiment.

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.

Definition 1.1.2 - Event

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

Union

Intersection

Complementation

Theorem 1.1.4 - Event Operations

Basics of Probability Theory

Conditional Probability and Independence

Random Variables

Distribution Functions

Density and Mass Functions