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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.

the generic structure of such models, and their basic properties. The models we consider assign probabilities to collections (sets) of possible outcomes. For this reason, we must begin with a short review of set theory. 1.1 SETS Probability makes extensive use of set operations, so let us introduce at the outset the relevant notation and ...

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