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Introduction to Probability - VFU

LECTURE NOTESC ourse 2000 Introduction to ProbabilityDimitri P. Bertsekas and John N. TsitsiklisProfessors of Electrical Engineering and Computer ScienceMassachusetts Institute of TechnologyCambridge, MassachusettsThese notes are copyright-protected but may be freely distributed forinstructional nonprofit Sample Space and Probability .. Sets .. Probabilistic Models .. Conditional Probability .. Independence .. Total Probability Theorem and Bayes Rule .. Counting.. Summary and Discussion ..2. Discrete Random Variables.. Basic Concepts .. Probability Mass Functions.. Functions of Random Variables .. Expectation, Mean, and Variance .. Joint PMFs of Multiple Random Variables .. Conditioning .. Independence .. Summary and Discussion ..3. General Random Variables.. Continuous Random Variables and PDFs .. Cumulative Distribution Functions .. Normal Random Variables .. Conditioning on an Event .. Multiple Continuous Random Variables.

on the basis of this empirical evidence, probability theory is an extremely useful tool. Our main objective in this book is to develop the art of describing un-certainty in terms of probabilistic models, as well as the skill of probabilistic reasoning. The first step, which is the subject of this chapter, is to describe

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