Advanced Probability Theory for Biomedical Engineers (eBook)

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.

John D. Enderle, Biomedical Engineering Program Director and Professor of Electrical & Computer Engineering at the University of Connecticut, received the B.S., M.E., and Ph.D. degrees in biomedical engineering, and M.E. degree in electrical engineering from Rensselaer Polytechnic Institute, Troy, New York, in 1975, 1977, 1980, and 1978, respectively. Dr. Enderle is a Fellow of the IEEE, the past Editor-in-Chief of the EMB Magazine (2002- 2008), the 2004 EMBS Service Award Recipient, Past-President of the IEEE-EMBS, and EMBS Conference Chair for the 22nd Annual International Conference of the IEEE EMBS and World Congress on Medical Physics and Biomedical Engineering in 2000. He is also a Fellow of the American Institute for Medical and Biological Engineering (AIMBE), Fellow of the American Society for Engineering Education and a Fellow of the Biomedical Engineering Society. Enderle is a former member of the ABET Engineering Accreditation Commission (2004-2009). In 2007, Enderle received the ASEE National Fred Merryfield Design Award. He is also a Teaching Fellow at the University of Connecticut since 1998.