Probability Foundations for Engineers

Suitable for a first course in probability theory and designed specifically for industrial engineering and operations management students, Probability Foundations for Engineers covers theory in an accessible manner and includes numerous practical examples based on engineering applications. Essentially, everyone understands and deals with probability every day in their normal lives. Nevertheless, for some reason, when engineering students who have good math skills are presented with the mathematics of probability theory, there is a disconnect somewhere. The book begins with a summary of set theory and then introduces probability and its axioms. The author has carefully avoided a theorem-proof type of presentation. He includes all of the theory but presents it in a conversational rather than formal manner, while relying on the assumption that undergraduate engineering students have a solid mastery of calculus. He explains mathematical theory by demonstrating how it is used with examples based on engineering applications. An important aspect of the text is the fact that examples are not presented in terms of "balls in urns". Many examples relate to gambling with coins, dice and cards but most are based on observable physical phenomena familiar to engineering students.

Historical PerspectivesFormal SystemsIntuitionExercisesA Brief Review of Set TheoryIntroductionDefinitionsSet OperationsVenn DiagramsDimensionalityConclusionExercisesProbability BasicsRandom Experiments, Outcomes, and EventsProbabilityProbability AxiomsConditional ProbabilityIndependenceExercisesRandom Variables and DistributionsRandom VariablesDistributionsDiscrete Distribution FunctionsContinuous Distribution FunctionsConditional ProbabilityHazard FunctionsIndependent Random VariablesExercisesJoint, Marginal, and Conditional DistributionsThe Idea of Joint Random VariablesThe Discrete CaseThe Continuous CaseIndependenceBivariate and Multivariate Normal DistributionsExercisesExpectation and Functions of Random VariablesExpectationThree Properties of ExpectationExpectation and Random VectorsConditional ExpectationGeneral Functions of Random VariablesExpectation and Functions of Multiple Random VariablesSums of Independent Random VariablesExercisesMoment-Generating FunctionsConstruction of the Moment-Generating FunctionConvolutionsJoint Moment-Generating FunctionsConditional Moment-Generating FunctionsExercisesApproximations and Limiting BehaviorDistribution-Free ApproximationsNormal and Poisson ApproximationsLaws of Large Numbers and the Central Limit TheoremExercisesAppendix: Cumulative Poisson ProbabilitiesIndex

Joel A. Nachlas serves on the faculty of the Grado Department of Industrial and Systems Engineering at Virginia Tech. He has taught at Virginia Tech since 1974 and acts as the coordinator for the department’s graduate program in Operations Research. For the past twelve years, he has also taught Reliability Theory regularly at the Ecole Superiore d'Ingenieures de Nice-Sophia Antipolis. Dr. Nachlas received his B. E. S. from the Johns Hopkins University in 1970, his M. S. in 1972 and his Ph. D. in 1976 both from the University of Pittsburgh. His research interests are in the applications of probability and statistics to problems in reliability and quality control. His work in microelectronics reliability has been performed in collaboration with and under the support of the IBM Corp., INTELSAT and the Bull Corp. He is the co-author of over fifty refereed articles, has served in numerous editorial and referee capacities and has lectured on reliability and maintenance topics throughout North America and Europe.