A First Course in Probability

The primary purpose of this book is to provide an introductory text for a one semester undergraduate course in probability. The only assumed background knowledge is that of calculus, which makes it suitable, not only for those following curricula in the mathematical sciences, but also for students whose future careers lie in diverse engineering fields, biological sciences, management science, among many others. The text covers all the probability concepts that are necessary for study in these areas and does so in a clear and methodical manner.Furthermore, the pedagogic approach that is adopted in this text, together with the more than 200 examples and worked exercises that are omnipresent and whose solutions are provided in great detail, enable students returning to school, after perhaps a brief period of time in industry, to master probability theory in a relatively short period of time.In chapter 1, trails, sample spaces, events, and the three probability axioms on which all of probability is based are introduced. From these concepts, conditional probability, independent events, the law of total probability and Bayes' rule are studied.Chapter 2 introduces combinatorics --- the art of counting. Permutations, with and without replacement, are studied as are combinations, again with and without replacement. The chapter concludes with an examination of sequences of Bernoulli trials.Random variables, both discrete and continuous, are studied in Chapter 3. Probability mass, probability density and cumulative distribution functions are introduced. We also study functions of a random variable and conditioned random variables.In Chapter 4, joint probability mass functions and joint cumulative distributions are introduced This is followed by an examination of conditional…