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The course is attended by a large number of students with diverse back grounds, and a broad range of interests. They span the entire spectrum from freshmen to beginning graduate students, and from the engineering school to the school of management. Accordingly, we have tried to strike a balance between simplicity in exposition and sophistication in analytical reasoning. Our key aim has been to develop the ability to construct and analyze probabilistic models in a manner that combines intuitive understanding and mathematical precision. In this spirit, some of the more mathematically rigorous analysis ha been just sketched or intuitively explained in the text. so that complex proofs do not stand in the way of an otherwise simple exposition. At the same time, some of this analysis is developed (at the level of advanced calculus) in theoretical problems, that are included at the end of the correspondingchapter.Frthermore,some of the subtler mathematical issues are hinted at in footnotes to the more attentive reader.