Basic Probability Theory with Applications - Lefebvre, Mario (Springer Undergraduate Texts in Mathematics and Technology, 2009)
This book presents elementary probability theory with interesting and well-chosen applications that illustrate the theory. An introductory chapter reviews the basic elements of differential calculus which are used in the material to follow. The theory is presented systematically, beginning with the main results in elementary probability theory. This is followed by material on random variables. Random vectors, including the all important central limit theorem, are treated next. The last three chapters concentrate on applications of this theory in the areas of reliability theory, basic queuing models, and time series. Examples are elegantly woven into the text and over 400 exercises reinforce the material and provide students with ample practice. This textbook can be used by undergraduate students in pure and applied sciences such as mathematics, engineering, computer science, finance and economics. A separate solutions manual is available to instructors who adopt the text for their course.