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Applied probability
OpenStax
@
Preface to pfeiffer applied probability
0.1
The course
0.2
A probability model
0.3
Matlab: a tool for learning
0.4
An invitation to experiment and explore
0.5
Acknowledgments
Probability systems
Likelihood
1
Probability systems
1.1
Probability measures
2
Interpretations
3
Problems on probability systems
Minterm analysis
Minterms
0.1
Introduction
0.2
Partitions and minterms
0.3
Minterm maps and the minterm expansion
0.4
Use of minterm maps
0.5
Survey on software
0.6
Systematic formulation
0.7
Indicator functions and the minterm expansion
1
Minterms and matlab calculations
1.1
Minterm vectors and matlab
1.2
The procedure mincalc
2
Problems on minterm analysis
Conditional probability
Conditional probability
1
Problems on conditional probability
Independence of events
Independence of events
1
Matlab and independent classes
2
Composite trials
3
Problems on independence of events
Conditional independence
Conditional independence
0.1
The concept
0.2
Buying umbrellas and the weather
0.3
Sixteen equivalent conditions
0.4
The use of independence techniques
1
Patterns of probable inference
1.1
Some patterns of probable inference
1.2
A market survey problem
1.3
A classification problem
1.4
A classification problem
1.5
Classification using frequency data
2
Problems on conditional independence
Random variables and probabilities
Random variables and probabilities
0.1
Introduction
0.2
Random variables as functions
0.3
Mass transfer and induced probability distribution
0.4
Simple random variables
0.5
Determination of the distribution
0.6
Finding the distribution from affine form
0.7
An m-procedure for determining the distribution from affine form
0.8
General random variables
1
Problems on random variables and probabilities
Distribution and density functions
Distribution and density functions
0.1
Introduction
0.2
The distribution function
0.3
Description of some common discrete distributions
0.4
The density function
0.5
Some common absolutely continuous distributions
1
Distribution approximations
2
Problems on distribution and density functions
Random vectors and joint distributions
Random vectors and joint distributions
0.1
Introduction
0.2
Random variables considered jointly; random vectors
0.3
Induced distribution and the joint distribution function
0.4
Marginal distributions
1
Random vectors and matlab
2
Problems on random vectors and joint distributions
Independent classes of random variables
Independent classes of random variables
1
Problems on independent classes of random variables
Functions of random variables
Functions of a random variable
1
Function of random vectors
1.1
The general approach extended to a pair
1.2
Use of matlab on pairs of simple random variables
1.3
Illustration of the basic joint calculations
1.4
Absolutely continuous case: analysis and approximation
2
The quantile function
2.1
The quantile function
3
Problems on functions of random variables
Mathematical expectation
Mathematical expectation: simple random variables
0.1
Introduction
0.2
Expectation for simple random variables
1
Mathematical expectation; general random variables
1.1
Extension to the general case
1.2
Properties and computation
1.3
Stocking for random demand (see Exercise 4 From "problems on functions
2
Problems on mathematical expectation
Variance, covariance, linear regression
Variance
1
Covariance and the correlation coefficient
1.1
Covariance and the correlation coefficient
2
Linear regression
2.1
Linear regression
3
Problems on variance, covariance, linear regression
Transform methods
Transform methods
1
Convergence and the central limit theorem
1.1
The central limit theorem
1.2
Convergence phenomena in probability theory
2
Simple random samples and statistics
2.1
Simple random samples and statistics
3
Problems on transform methods
Conditional expectation, regression
Conditional expectation, regression
0.1
Conditioning by an event
0.2
Conditioning by a random vector—discrete case
0.3
Basic calculations and interpretation
0.4
Conditioning by a random vector — absolutely continuous case
0.5
Extension to the general case
0.6
The regression problem
1
Problems on conditional expectation, regression
Random selection
Random selection
1
Some random selection problems
2
Problems on random selection
Conditional independence, given a random vector
Conditional independence, given a random vector
1
Elements of markov sequences
1.1
Elements of markov sequences
1.2
Branching process continued
1.3
Inventory problem (continued)
1.4
The long run distribution for the inventory example
1.5
Simulation of finite homogeneous markov sequences
2
Problems on conditional independence, given a random vector
Appendices
Appendix a to applied probability: directory of m-functions and m
0.1
Matlab features
0.2
Auxiliary user-defined building blocks
0.3
Minterm vectors and probabilities
0.4
Independent events
0.5
Conditional probability and conditional idependence
0.6
Bernoulli and multinomial trials
0.7
Some matching problems
0.8
Distributions
0.9
Binomial, poisson, and gaussian dstributions
0.10
Setup for simple random variables
0.11
Setup for general random variables
0.12
Setup for independent simple random variables
0.13
Calculations for random variables
0.14
Calculations and tests for independent random variables
0.15
Quantile functions for bounded distributions
0.16
Compound demand
0.17
Simulation of markov systems
1
Appendix b to applied probability: some mathematical aids
1.1
Series
1.2
Some useful integrals
1.3
Some basic counting problems
1.4
Extended binomial coefficients and the binomial series
1.5
Cauchy's equation
1.6
Countable and uncountable sets
2
Appendix c: data on some common distributions
3
Appendix d to applied probability: the standard normal distribution
4
Appendix e to applied probability: properties of mathematical expectation
5
Appendix f to applied probability: properties of conditional expectation
6
Appendix g to applied probability: properties of conditional independence
7
Matlab files for "problems" in "applied probability"
7.1
Npr02_04
7.2
Npr02_05
7.3
Npr02_06
7.4
Npr02_07
7.5
Npr02_08
7.6
Npr02_09
7.7
Npr02_10
7.8
Npr02_11
7.9
Npr02_12
7.10
Npr02_13
7.11
Npr02_14
7.12
Npr02_15
7.13
Npr02_16
7.14
Npr02_17
7.15
Npr02_18
7.16
Npr02_19
7.17
Npr02_20
7.18
Npr02_21
7.19
Npr02_22
7.20
Npr02_23
7.21
Npr03_01
7.22
Npr04_04
7.23
Npr04_05
7.24
Npr04_06
7.25
Mpr05_16
7.26
Npr05_17
7.27
Npr06_10
7.28
Npr06_12
7.29
Npr06_18.m
7.30
Npr07_01
7.31
Npr07_02
7.32
Npr08_01
7.33
Npr08_02
7.34
Npr08_03
7.35
Npr08_04
7.36
Npr08_05
7.37
Npr08_06
7.38
Npr08_07
7.39
Npr08_08
7.40
Npr08_09
7.41
Npr09_02
7.42
Npr10_16
7.43
Npr12_10
7.44
Npr16_07
7.45
Npr16_09
Source:
OpenStax, Applied probability. OpenStax CNX. Aug 31, 2009 Download for free at http://cnx.org/content/col10708/1.6
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