Bertsekas_ Tsitsiklis. Introduction to probability (MIT lecture notes_ 2000)(284s)

Bertsekas_ Tsitsiklis. Introduction to probability (MIT lecture notes_ 2000)(284s)

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Unformatted text preview: LECTURE NOTES Course 6.041-6.431 M.I.T. FALL 2000 Introduction to Probability Dimitri P. Bertsekas and John N. Tsitsiklis Professors of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge, Massachusetts These notes are copyright-protected but may be freely distributed for instructional nonprot pruposes. Contents 1. Sample Space and Probability . . . . . . . . . . . . . . . . 1.1. Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2. Probabilistic Models . . . . . . . . . . . . . . . . . . . . . . . 1.3. Conditional Probability . . . . . . . . . . . . . . . . . . . . . 1.4. Independence . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5. Total Probability Theorem and Bayes Rule . . . . . . . . . . . . 1.6. Counting . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7. Summary and Discussion . . . . . . . . . . . . . . . . . . . . 2. Discrete Random Variables . . . . . . . . . . . . . . . . . 2.1. Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Probability Mass Functions . . . . . . . . . . . . . . . . . . . 2.3. Functions of Random Variables . . . . . . . . . . . . . . . . . . 2.4. Expectation, Mean, and Variance . . . . .. . . . . . . . . . . . 2.5. Joint PMFs of Multiple Random Variables . . . . . . . . . . . . . 2.6. Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7. Independence . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8. Summary and Discussion . . . . . . . . . . . . . . . . . . . . 3. General Random Variables . . . . . . . . . . . . . . . . . 3.1. Continuous Random Variables and PDFs . . . . . . . . . . . . . 3.2. Cumulative Distribution Functions . . . . . . . . . . . . . . . . 3.3. Normal Random Variables . . . . . . . . . . . . . . . . . . . . 3.4. Conditioning on an Event . . . . . . .. . . . . . . . . . . . . 3.5. Multiple Continuous Random Variables . . . . . . . . . . . . . . 3.6. Derived Distributions . . . . . . . . . . . . . . . . . . . . . . 3.7. Summary and Discussion . . . . . . . . . . . . . . . . . . . . 4. Further Topics on Random Variables and Expectations . . . . . . 4.1. Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Sums of Independent Random Variables - Convolutions . . . . . . . iii iv Contents 4.3. Conditional Expectation as a Random Variable . . . . . . . . . . . 4.4. Sum of a Random Number of Independent Random Variables . . . . 4.5. Covariance and Correlation . . . . . . . . . . . . . . . . . . . 4.6. Least Squares Estimation . . . . . . . . . . . . . . . . . . . . 4.7. The Bivariate Normal Distribution . . . . . . . . . . . . . . . . 5. The Bernoulli and Poisson Processes . . . . . . . . . . . . . ....
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Bertsekas_ Tsitsiklis. Introduction to probability (MIT lecture notes_ 2000)(284s)

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