Probability Theory

This book provides a systematic, self-sufficient and yet short presentation of the mainstream topics on introductory Probability Theory with some selected topics from Mathematical Statistics. It is suitable for a 10- to 14-week course for second- or third-year undergraduate students in Science, Mathematics, Statistics, Finance, or Economics, who have completed some introductory course in Calculus. There is a sufficient number of problems and solutions to cover weekly tutorials.

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Contents:ProbabilityRandom VariablesJoint DistributionsTransformations of the DistributionsExpectation of Random VariablesVariance and CovarianceConditional ExpectationsMoment Generating FunctionsAnalysis of Some Important DistributionsLimit TheoremsStatistical Inference: Point EstimationStatistical Inference: Interval EstimationAppendices:Solutions for the Problems for Weeks 1–12Sample Problems for Final ExamsSome Bonus Challenging ProblemsStatistical Tables
Readership: Undergraduate students, teachers and lecturers in Mathematics and Statistics.

Key Features:This book is short and comprehensiveThe amount of material is exactly as is needed for a one-semester courseThere are enough problems with solutions to cover weekly tutorialsSupplementary PDF files of presentation slides are provided for lecturers who adopt the textbook