Basic Probability Theory For Biomedical Engineers

This is the first in a series of short books on probability theory and random processes for biomedical engineers. This text is written as an introduction to probability theory. The goal was to prepare students, engineers and scientists at all levels of background and experience for the application of this theory to a wide variety of problems--as well as pursue these topics at a more advanced level. The approach is to present a unified treatment of the subject. There are only a few key concepts involved in the basic theory of probability theory. These key concepts are all presented in the first chapter. The second chapter introduces the topic of random variables. Later chapters simply expand upon these key ideas and extend the range of application. A considerable effort has been made to develop the theory in a logical manner--developing special mathematical skills as needed. The mathematical background required of the reader is basic knowledge of differential calculus. Every effort has been made to be consistent with commonly used notation and terminology--both within the engineering community as well as the probability and statistics literature. Biomedical engineering examples are introduced throughout the text and a large number of self-study problems are available for the reader.

This is the third in a series of short books on probability theory and random processes for biomedical engineers. This book focuses on standard probability distributions commonly encountered in biomedical engineering. The exponential, Poisson and Gaussian distributions are introduced, as well as important approximations to the Bernoulli PMF and Gaussian CDF. Many important properties of jointly Gaussian random variables are presented. The primary subjects of the final chapter are methods for determining the probability distribution of a function of a random variable. We first evaluate the probability distribution of a function of one random variable using the CDF and then the PDF. Next, the probability distribution for a single random variable is determined from a function of two random variables using the CDF. Then, the joint probability distribution is found from a function of two random variables using the joint PDF and the CDF. The aim of all three books is as an introduction to probability theory. The audience includes students, engineers and researchers presenting applications of this theory to a wide variety of problems—as well as pursuing these topics at a more advanced level. The theory material is presented in a logical manner—developing special mathematical skills as needed. The mathematical background required of the reader is basic knowledge of differential calculus. Pertinent biomedical engineering examples are throughout the text. Drill problems, straightforward exercises designed to reinforce concepts and develop problem solution skills, follow most sections.

This is the first in a series of short books on probability theory and random processes for biomedical engineers. This text is written as an introduction to probability theory. The goal was to prepare students, engineers and scientists at all levels of background and experience for the application of this theory to a wide variety of problems—as well as pursue these topics at a more advanced level. The approach is to present a unified treatment of the subject. There are only a few key concepts involved in the basic theory of probability theory. These key concepts are all presented in the first chapter. The second chapter introduces the topic of random variables. Later chapters simply expand upon these key ideas and extend the range of application. A considerable effort has been made to develop the theory in a logical manner—developing special mathematical skills as needed. The mathematical background required of the reader is basic knowledge of differential calculus. Every effort has been made to be consistent with commonly used notation and terminology—both within the engineering community as well as the probability and statistics literature. Biomedical engineering examples are introduced throughout the text and a large number of self-study problems are available for the reader.

This is the second in a series of three short books on probability theory and random processes for biomedical engineers. This volume focuses on expectation, standard deviation, moments, and the characteristic function. In addition, conditional expectation, conditional moments and the conditional characteristic function are also discussed. Jointly distributed random variables are described, along with joint expectation, joint moments, and the joint characteristic function. Convolution is also developed. A considerable effort has been made to develop the theory in a logical manner—developing special mathematical skills as needed. The mathematical background required of the reader is basic knowledge of differential calculus. Every effort has been made to be consistent with commonly used notation and terminology—both within the engineering community as well as the probability and statistics literature. The aim is to prepare students for the application of this theory to a wide variety of problems, as well give practicing engineers and researchers a tool to pursue these topics at a more advanced level. Pertinent biomedical engineering examples are used throughout the text.

This is the second in a series of three short books on probability theory and random processes for biomedical engineers. This volume focuses on expectation, standard deviation, moments, and the characteristic function. In addition, conditional expectation, conditional moments and the conditional characteristic function are also discussed. Jointly distributed random variables are described, along with joint expectation, joint moments, and the joint characteristic function. Convolution is also developed. A considerable effort has been made to develop the theory in a logical manner—developing special mathematical skills as needed. The mathematical background required of the reader is basic knowledge of differential calculus. Every effort has been made to be consistent with commonly used notation and terminology—both within the engineering community as well as the probability and statistics literature. The aim is to prepare students for the application of this theory to a wide variety of problems, as well give practicing engineers and researchers a tool to pursue these topics at a more advanced level. Pertinent biomedical engineering examples are used throughout the text.

Intended as an introduction to the field of biomedical engineering, this book covers the topics of biomechanics (Part I) and bioelectricity (Part II). Each chapter emphasizes a fundamental principle or law, such as Darcy's Law, Poiseuille's Law, Hooke's Law, Starling's Law, levers, and work in the area of fluid, solid, and cardiovascular biomechanics. In addition, electrical laws and analysis tools are introduced, including Ohm's Law, Kirchhoff's Laws, Coulomb's Law, capacitors and the fluid/electrical analogy. Culminating the electrical portion are chapters covering Nernst and membrane potentials and Fourier transforms. Examples are solved throughout the book and problems with answers are given at the end of each chapter. A semester-long Major Project that models the human systemic cardiovascular system, utilizing both a Matlab numerical simulation and an electrical analog circuit, ties many of the book's concepts together.

This book provides the reader with the basic skills and tools of statistics and probability in the context of engineering modeling and analysis. The emphasis is on the application and the reasoning behind the application of these skills and tools for the purpose of enhancing decision making in engineering. The purpose of the book is to ensure that the reader will acquire the required theoretical basis and technical skills such as to feel comfortable with the theory of basic statistics and probability. Moreover, in this book, as opposed to many standard books on the same subject, the perspective is to focus on the use of the theory for the purpose of engineering model building and decision making. This work is suitable for readers with little or no prior knowledge on the subject of statistics and probability.

Intended as an introduction to the field of biomedical engineering, this book covers the topics of biomechanics (Part I) and bioelectricity (Part II). Each chapter emphasizes a fundamental principle or law, such as Darcy's Law, Poiseuille's Law, Hooke's Law, Starling's Law, levers, and work in the area of fluid, solid, and cardiovascular biomechanics. In addition, electrical laws and analysis tools are introduced, including Ohm's Law, Kirchhoff's Laws, Coulomb's Law, capacitors and the fluid/electrical analogy. Culminating the electrical portion are chapters covering Nernst and membrane potentials and Fourier transforms. Examples are solved throughout the book and problems with answers are given at the end of each chapter. A semester-long Major Project that models the human systemic cardiovascular system, utilizing both a Matlab numerical simulation and an electrical analog circuit, ties many of the book's concepts together. Table of Contents: Basic Concepts / Darcy's Law / Poiseuille's Law: Pressure-Driven Flow Through Tubes / Hooke's Law: Elasticity of Tissues and Compliant Vessels / Starling's Law of the Heart, Windkessel Elements and Volume / Euler's Method and First-Order Time Constants / Muscle, Leverage, Work, Energy and Power

The theory of probability and mathematical statistics is becoming an indispensable discipline in many branches of science and engineering. This is caused by increasing significance of various uncertainties affecting performance of complex technological systems. Fundamental concepts and procedures used in analysis of these systems are often based on the theory of probability and mathematical statistics. The book sets out fundamental principles of the probability theory, supplemented by theoretical models of random variables, evaluation of experimental data, sampling theory, distribution updating and tests of statistical hypotheses. Basic concepts of Bayesian approach to probability and two-dimensional random variables, are also covered. Examples of reliability analysis and risk assessment of technological systems are used throughout the book to illustrate basic theoretical concepts and their applications. The primary audience for the book includes undergraduate and graduate students of science and engineering, scientific workers and engineers and specialists in the field of reliability analysis and risk assessment. Except basic knowledge of undergraduate mathematics no special prerequisite is required.

This is Volume 2 in the Synthesis Lectures on Biomedical Engineering combined series, which includes four Synthesis lectures in one volume. This volume includes the following short books: Fundamentals of Respiratory System and Sounds Analysis / Basic Probability Theory for Biomedical Engineers / Intermediate Probability Theory for Biomedical Engineers / Advanced Probability Theory for Biomedical Engineers