Advanced Probability Theory for Biomedical Engineers

PDF | English | 1MB | 108 Pages

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.


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