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# Applied Probability

By Paul Pfeiffer
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Book Description

The present collection utilizes a number of user defined m-programs, in combination with built in MATLAB functions, for solving a variety of probabilistic problems. These m-files are included as text files in the collection New Prob m-files. We use the term m-function to designate a user-defined function as distinct from the basic MATLAB functions which are part of the MATLAB package. An m-procedure (or sometimes a procedure) is an m-file containing a set of MATLAB commands which carry out a prescribed set of operations. Generally, these will prompt for (or assume) certain data upon which the procedure is carried out. We use the term m-program (or often m-file) to refer to either an m-function or an m-procedure. Although most of the m-programs were written for MATLAB version 4.2, they work for versions 5.1, 5.2, and 7.04. The latter versions offer some new features which may make more efficient implementation of some of the m-programs, and which make possible some new ones. With one exception (so noted), these are not exploited in this collection, because of the pedagogical value of dealing with explicitly developed procedures whose dependence on basic MATLAB is displayed. These programs, with perhaps some exceptions, also run on the MATLAB alternatives SCILAB and OCTAVE. Users of these latter programs should be able to make appropriate adjustments if needed. In addition to the m-programs there is a collection of m-files for specific problems with properly formatted data which can be entered into the workspace by calling the file. These m-files come from a variety of sources ( e.g., exams or problem sets, hence the odd names) and may be useful for examples and exercises. This collection is in the text file New Prob mfiles.

• Applied Probability
• Preface to Pfeiffer Applied Probability
• 1. Probability Systems
• 2. Minterm Analysis
• 3. Conditional Probability
• 4. Independence of Events
• 5. Conditional Independence
• 6. Random Variables and Probabilities
• 7. Distribution and Density Functions
• 8. Random Vectors and joint Distributions
• 9. Independent Classes of Random Variables
• 10. Functions of Random Variables
• 11. Mathematical Expectation
• 12. Variance, Covariance, Linear Regression
• 13. Transform Methods
• 14. Conditional Expectation, Regression
• 15. Random Selection
• 16. Conditional Independence, Given a Random Vector
• 17. Appendices
• Index
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