Probability Foundations for Electrical Engineers

Por: Swayam . en: , ,

Week 1: Introduction, Cardinality and Countability, Probability SpaceWeek 2: Properties of Probability Space, Discrete Probability Space, Generated sigma-algebraWeek 3: Borel sets, Caratheodory’s extension theorem, Lebesgue Measure, Infinite coin toss modelWeek 4: Conditional probability, Independence, Borel-Cantelli LemmasWeek 5: Random variables, Distribution function, Types of random variablesWeek 6: Discrete Random variables, Continuous random variables, Singular random variablesWeek 7: Several random variables, joint distribution, independent random variablesWeek 8: Transformation of random variablesWeek 9: Integration and Expectation, properties of integrals, Monotone convergence, Dominated convergence, Expectation over different spacesWeek 10:Variance, covariance, and conditional expectationWeek 11:Transform techniques: moment generating function, characteristic functionWeek 12:Convergence of random variables, Laws of large numbers, Central limit theorem