I Basic Probability. - 1 Trials and Events. - 2 Probability Systems. - 2a The Sigma Algebra of Events. - 3 Conditional Probability. - 4 Independence of Events. - 5 Conditional Independence of Events. - 6 Composite Trials. - II Random Variables and Distributions. - 7 Random Variables and Probabilities. - 7a Borel Sets Random Variables and Borel Functions. - 8 Distribution and Density Functions. - 9 Random Vectors and Joint Distributions. - 10 Independence of Random Vectors. - 11 Functions of Random Variables. - 11a Some Properties of the Quantile Function. - III Mathematical Expectation. - 12 Mathematical Expectation. - 13 Expectation and Integrals. - 13a Supplementary Theoretical Details. - 14 Properties of Expectation. - 15 Variance and Standard Deviation. - 16 Covariance Correlation and Linear Regression. - 17 Convergence in Probability Theory. - 18 Transform Methods. - IV Conditional Expectation. - 19 Conditional Expectation Given a Random Vector. - 19a Some Theoretical Details. - 20 Random Selection and Counting Processes. - 21 Poisson Processes. - 21a. - 22 Conditional Independence Given a Random Vector. - 22a Proofs of Properties. - 23 Markov Sequences. - 23a Some Theoretical Details. - A Some Mathematical Aids. - B Some Basic Counting Problems. Language: English