概率论——不确定性的科学

Cours

Chinois

Source

Sur www.xuetangx.com

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Niveau Introductif

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Détails du cours

Déroulé

Unit 0: Overview: Lec. 0: Course overview; Course introduction, objectives, and study guide; Syllabus, calendar, and grading policy; edX Tutorial; Discussion forum and collaboration guidelines; Homework mechanics and standard notation

Entrance Survey: Important Preliminary Survey

Unit 1: Probability models and axioms: Lec. 1: Probability models and axioms; Mathematical background
Sets; sequences, limits, and series; (un)countable sets.; Solved problems; Problem Set 1; Unit 1 Discussion forums

Unit 2: Conditioning and independence: Unit overview; Lec. 2: Conditioning and Bayes' rule; Lec. 3: Independence; Solved problems; Problem Set 2

Unit 3: Counting: Lec. 4: Counting; Solved problems; Problem Set 3

Unit 4: Discrete random variables: Unit overview; Lec. 5: Probability mass functions and expectations; Lec. 6: Variance; Conditioning on an event; Multiple r.v.'s; Lec. 7: Conditioning on a random variable; Independence of r.v.'s; Solved problems; Additional theoretical material; Problem Set 4; Unit summary

Exam 1: Exam 1

Unit 5: Continuous random variables: Unit overview; Lec. 8: Probability density functions; Lec. 9: Conditioning on an event; Multiple r.v.'s; Lec. 10: Conditioning on a random variable; Independence; Bayes' rule; Standard normal table; Solved problems; Problem Set 5; Unit summary

Unit 6: Further topics on random variables: Unit overview; Lec. 11: Derived distributions; Lec. 12: Sums of independent r.v.'s; Covariance and correlation; Lec. 13: Conditional expectation and variance revisited; Sum of a random number of independent r.v.'s; Solved problems; Additional theoretical material; Problem Set 6; Unit summary

Unit 7: Bayesian inference: Unit overview; Lec. 14: Introduction to Bayesian inference; Lec. 15: Linear models with normal noise; Problem Set 7a; Lec. 16: Least mean squares (LMS) estimation; Lec. 17: Linear least mean squares (LLMS) estimation; Problem Set 7b; Solved problems; Additional theoretical material; Unit summary

Exam 2: Exam 2

Unit 8: Limit theorems and classical statistics: Unit overview; Lec. 18: Inequalities, convergence, and the Weak Law of Large Numbers; Lec. 19: The Central Limit Theorem (CLT); Lec. 20: An introduction to classical statistics; Solved problems; Additional theoretical material; Problem Set 8; Unit summary

Unit 9: Bernoulli and Poisson processes: Unit overview; Lec. 21: The Bernoulli process; Lec. 22: The Poisson process; Lec. 23: More on the Poisson process; Solved problems; Additional theoretical material; Problem Set 9; Unit summary

Unit 10: Markov chains: Unit overview; Lec. 24: Finite-state Markov chains; Lec. 25: Steady-state behavior of Markov chains; Lec. 26: Absorption probabilities and expected time to absorption; Solved problems; Problem Set 10

Exit Survey: Important Exit Survey

Final Exam: Final Exam

Prérequis

Aucun.

Intervenants

John Tsitsiklis

Plateforme

Fondée par l'Université Tsinghua en octobre 2013, XuetangX est la première plateforme MOOC chinoise au monde et sert de plate-forme de recherche et d'application au Centre de recherche pour la formation en ligne du ministère de l'Éducation. XuetangX a été primé parmi le premier groupe national de projets de base de démonstration pour l'innovation et l'entrepreneuriat. Par ailleurs, XuetangX collabore également avec le Centre international de formation des ingénieurs (ICEE) sous les auspices de l’UNESCO et soutient sa partie en ligne. À la fin de juin 2018, avec un total de 25 millions d'inscriptions et plus de 1 500 cours en ligne dans 13 disciplines différentes, XuetangX a accumulé plus de 12 millions d'utilisateurs enregistrés, répartis dans 209 pays et régions.

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