Basic Concept Of Probability

Introduction ,[object Object],[object Object]

Simple Games Involving Probability ,[object Object],[object Object]

Random Experiment ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Events & Sample Spaces Sample Space The sample space is the set of all possible outcomes. Simple Events The individual outcomes are called simple events. Event An event is any collection of one or more simple events

Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Basic Concepts (from Set Theory) ,[object Object],[object Object],[object Object],[object Object]

Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Rules ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Venn Diagram ,[object Object],A B A ∩B

Probability ,[object Object],[object Object]

Axioms of Probability ,[object Object],[object Object],[object Object],[object Object],[object Object]

Properties of Probability ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example ,[object Object],[object Object],[object Object],[object Object]

Intuitive Development (agrees with axioms) ,[object Object],Where N(a) is the number that event a happens in n trials

Here We Go Again: Not So Basic Probability

More Formal: ,[object Object],[object Object],[object Object],[object Object]

Independence ,[object Object],[object Object],A and B are independent, if knowing that A has happened does not say anything about B happening

Bayes Theorem ,[object Object]

Conditional Probability ,[object Object],A B 

Using Partitions: ,[object Object]

Random Variables ,[object Object],  X(  )

Random Variables Distributions ,[object Object],[object Object]

Random Distributions: ,[object Object]

Uniform Distribution ,[object Object],X 1 X 2

Gaussian (Normal) Distribution ,[object Object],

Statistical Characterizations ,[object Object],[object Object]

Mean Estimation from Samples ,[object Object]

Variance Estimation from Samples ,[object Object]

Chapter 1: Introduction to Pattern Recognition (Sections 1.1-1.6) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Machine Perception ,[object Object],[object Object],[object Object],[object Object],[object Object]

An Example ,[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object]

[object Object],[object Object],[object Object]

[object Object],[object Object],Lightness Width

Basic Concept Of Probability

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