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Applied Probability by Paul E Pfeiffer - HTML preview
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Applied Probability
Table of Contents
Preface to Pfeiffer Applied Probability
1
.
The course
A probability model
MATLAB: A tool for learning
An Invitation to Experiment and Explore
Acknowledgments
Chapter
1
.
Probability Systems
1.1
.
Likelihood
Introduction
Outcomes and events
1.2
.
Probability Systems
Probability measures
1.3
.
Interpretations
What is Probability?
Probability and odds
Partitions and Boolean combinations of events
The indicator function
A technical comment on the class of events
1.4
.
Problems on Probability Systems
Chapter
2
.
Minterm Analysis
2.1
.
Minterms
Introduction
Partitions and minterms
Minterm maps and the minterm expansion
Use of minterm maps
Systematic formulation
Indicator functions and the minterm expansion
2.2
.
Minterms and MATLAB Calculations
Minterm vectors and MATLAB
The procedure mincalc
2.3
.
Problems on Minterm Analysis
Chapter
3
.
Conditional Probability
3.1
.
Conditional Probability
Introduction
Conditional probability
Some properties
Repeated conditioning
3.2
.
Problems on Conditional Probability
Chapter
4
.
Independence of Events
4.1
.
Independence of Events
Independence as lack of conditioning
Independent pairs
Independent classes
4.2
.
MATLAB and Independent Classes
MATLAB and Independent Classes
Probabilities of Boolean combinations
Independent Boolean combinations
4.3
.
Composite Trials
Composite trials and component events
Bernoulli trials and the binomial distribution
Joint Bernoulli trials
Alternate MATLAB implementations
4.4
.
Problems on Independence of Events
Chapter
5
.
Conditional Independence
5.1
.
Conditional Independence
The concept
Sixteen equivalent conditions
The use of independence techniques
5.2
.
Patterns of Probable Inference
Some Patterns of Probable Inference
A classification problem
5.3
.
Problems on Conditional Independence
Chapter
6
.
Random Variables and Probabilities
6.1
.
Random Variables and Probabilities
Introduction
Random variables as functions
Mass transfer and induced probability distribution
Simple random variables
Determination of the distribution
An m-procedure for determining the distribution from affine form
General random variables
6.2
.
Problems on Random Variables and Probabilities
Chapter
7
.
Distribution and Density Functions
7.1
.
Distribution and Density Functions
Introduction
The distribution function
Description of some common discrete distributions
The density function
Some common absolutely continuous distributions
7.2
.
Distribution Approximations
Binomial, Poisson, gamma, and Gaussian distributions
Approximation of a real random variable by simple random variables
7.3
.
Problems on Distribution and Density Functions
Chapter
8
.
Random Vectors and joint Distributions
8.1
.
Random Vectors and Joint Distributions
Introduction
Random variables considered jointly; random vectors
Induced distribution and the joint distribution function
Marginal distributions
8.2
.
Random Vectors and MATLAB
m-procedures for a pair of simple random variables
Joint absolutely continuous random variables
Discrete approximation in the continuous case
8.3
.
Problems On Random Vectors and Joint Distributions
Chapter
9
.
Independent Classes of Random Variables
9.1
.
Independent Classes of Random Variables
Introduction
Independent pairs
The joint mass distribution
Independent classes
Simple random variables
Approximation for the absolutely continuous case
9.2
.
Problems on Independent Classes of Random Variables
Chapter
10
.
Functions of Random Variables
10.1
.
Functions of a Random Variable
The problem; an approach
Use of MATLAB on simple random variables
10.2
.
Function of Random Vectors
The general approach extended to a pair
Use of MATLAB on pairs of simple random variables
Absolutely continuous case: analysis and approximation
10.3
.
The Quantile Function
The Quantile Function
10.4
.
Problems on Functions of Random Variables
Chapter
11
.
Mathematical Expectation
11.1
.
Mathematical Expectation: Simple Random Variables
Introduction
Expectation for simple random variables
11.2
.
Mathematical Expectation; General Random Variables
Extension to the General Case
Properties and computation
11.3
.
Problems on Mathematical Expectation
Chapter
12
.
Variance, Covariance, Linear Regression
12.1
.
Variance
Variance
12.2
.
Covariance and the Correlation Coefficient
Covariance and the Correlation Coefficient
12.3
.
Linear Regression
Linear Regression
12.4
.
Problems on Variance, Covariance, Linear Regression
Chapter
13
.
Transform Methods
13.1
.
Transform Methods
Three basic transforms
Integral transforms
13.2
.
Convergence and the central Limit Theorem
The Central Limit Theorem
Convergence phenomena in probability theory
13.3
.
Simple Random Samples and Statistics
Simple Random Samples and Statistics
13.4
.
Problems on Transform Methods
Chapter
14
.
Conditional Expectation, Regression
14.1
.
Conditional Expectation, Regression
Conditioning by an event
Conditioning by a random vector—discrete case
Conditioning by a random vector — absolutely continuous case
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