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概率论——不确定性的科学
Course
zh
Chinese
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- Introductive Level
Course details
Syllabus
- 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
Prerequisite
None.
Instructors
- John Tsitsiklis
Platform
Founded by Tsinghua University in October 2013, XuetangX is the world’s first Chinese MOOC platform and serves as the research and application platform for the Ministry of Education (MOE) Research Center for Online Education. XuetangX has been awarded as one of the national first batch of demonstration base projects for innovation and entrepreneurship. Besides, XuetangX also works with the International Center for Engineering Education (ICEE) under the auspices of UNESCO and supports its online portion. By the end of June 2018, with a total of 25 million enrollments and more than 1,500 online courses from 13 disciplined fields, XuetangX has accumulated over 12 million registered users, covering 209 countries and regions.
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