Probability Concepts and Theory for Engineers

by Schwarzlander , Harry

• ISBN13: 9780470748558
• ISBN10: 0470748559
• Edition: 1st
• Format: Hardcover
• Copyright: 2011-02-21
• Publisher: Wiley

Summary

This book aims to get the electrical and electronic engineering student well versed in the 'machinery' of probability theory. It steers clear of getting into application areas any more than is needed to get the reader comfortable with the mathematics and connecting it to models of practical situations. The author has elaborated and expanded upon his teaching notes, developed over a number of years with feedback from his students. Classroom tested, this book should cover everything that is required by the electrical engineering student of today, and with a solutions manual accompanying, the book will be perfect for teaching purposes. First book aimed specifically at electrical and electronic engineering graduates to adequately explain the basic models and rules for applying probability theory to engineering Unique presentation 86 Sections, each ending with shortanswer review questions, are divided into 6 Parts making the material&nbs

Author Biography

Professor Harry Schwarzlander, Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, New York, USA
Harry Schwarzlander is Associate Professor Emeritus at Syracuse University and has been with the university since 1964 where he has developed and taught 25 courses to electrical engineering graduate and undergraduate students. He was an Instructor in the Department of Electrical Engineering at Purdue University from 1960 to 1964, and before that, an Engineer and Project Engineer for General Electronic Laboratories, Inc., Cambridge, Massachusetts.
Professor Schwarzlander is a Registered Professional Engineer in New York and a Life Member of IEEE, taking posts as Secretary and Chairman between 1967 and 1969. In 2004 he was awarded Doctor Honoris Causa 'in recognition of outstanding accomplishments, exemplary educational leadership and distinguished service to mankind' by The International Institute for Advanced Studies in Systems Research and Cybernetics. He holds one patent for the RMS-Measuring Voltmeter, 1959.
Currently Executive Director of The New Environment, Inc. and Editor of New Environment Bulletin (the monthly newsletter of the New Environment Association), Professor Schwarzlander has contributed to over 65 publications and presentations. He researches into a range of different areas, including interference testing of electronic equipment and information storage and retrieval.

Table of Contents

The Basic Model

Introduction to Part I

Dealing with 'Real World' Problems

The Probabilistic Experiment

Outcomes

Events

The Connection to the Mathematical World

Elements and Sets

Classes of Sets

Elementary Set Operations

Additional Set Operations

Functions

The Size of a Set

Multiple and Infinite Set Operations

More About Additive Classes

Additive Set Functions

More about Probabilistic Experiments

The Probability Function

Probability Space

Simple Probability Arithmetic

Summary of Part I

The Approach to Elementary Probability Problems

Introduction to Part II

About Probability Problems

Equally Likely Possible Outcomes

Conditional Probability

Conditional Probability Distributions

Independent Events

Classes of Independent Events

Possible Outcomes Represented as Ordered k-tuples

Product Experiments and Product Spaces

Product Probability Spaces

Dependence Between the Components in an Ordered k-tuple

Multiple Observations Without Regard to Order

Unordered Sampling with Replacement

More Complicated Discrete Probability Problems

Uncertainty and Randomness

Fuzziness

Summary of Part II

Introduction to Random Variables

Introduction to Part III

Numerical-Valued Outcomes

The Binomial Distribution

The Real Numbers

General Definition of a Random Variable

The Cumulative Distribution Function

The Probability Density Function

The Gaussian Distribution

Two Discrete Random Variables

Two Arbitrary Random Variables

Two-Dimensional Distribution Functions

Two-Dimensional Density Functions

Two Statistically Independent Random Variables

Two Statistically Independent R.V.'s - Absolutely Continuous Case

Summary of Part III

Transformations and Multiple Random Variables

Introduction to Part IV

Transformation of a Random Variable

Transformation of a Two-Dimensional Random Variable

The Sum of Two Discrete Random Variables

The Sum of Two Arbitrary Random Variables

n-Dimensional Random Variables

Absolutely Continuous n-Dimensional Random Variables

Coordinate Transformations

Rotations and the Bivariate Gaussian Distribution

Several Statistically Independent RandomVariables

Singular Distributions in One Dimension

Conditional Induced Distribution, Given an Event

Resolving a Distribution into Components of Pure Type

Conditional Distribution Given the Value of a Random Variable

Random Occurrences in Time

Summary of Part IV

Parameters For Describing R.V.'s and Induced Distributions

Introduction to Part V

Some Properties of a Random Variable

Higher Moments

Expectation of a Function of a Random Variable

The Variance of a Function of a Random Variable

Bounds on the Induced Distribution

Test Sampling

Conditional Expectation With Respect to an Event

Covariance and Correlation Coefficient

The Correlation Coefficient as Parameter in a Joint Distribution

More General Kinds of Dependence Between Random Variables

The Covariance Matrix

Random Variables as the Elements of a Vector Space

Estimation

The Stieltjes Integral

Summary of Part V

Further Topics in Random Variables

Introduction to Part VI

Complex Random Variables

The Characteristic Function

Characteristic Function of a Transformed Random Variable

Characteristic Function of a Multi-Dimensional R.V

The Generating Function

Several Jointly Gaussian Random Variables

Spherically Symmetric Vector R.V.'s

Entropy Associated with Random Variables

Copulas

Sequences of Random Variables

Convergence of Sequences

Convergence of Probability Distributions and the Central Limit Theorem

Summary of Part VI

Appendix

Table of Query Solutions

Table of Gaussian Integral

Problems for PART I

Problems for PART II

Problems for PART III

Problems for PART IV

Problems for PART V

Problems for PART VI

Notation and Abbreviations

References

Index

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