MITx: ] 6.431x Probability - The Science of Uncertainty and Data
- Code: Tout sélectionner
6.431x Fall 2018 Syllabus
Unit 0: Overview (released Tue. August 28)
Unit 1: Probability models and axioms (released Mon. Sep 3; Sections 1.1-1.2)
L1: Probability models and axioms
Problem Set 1 due on Tue Sept 11
Unit 2: Conditioning and independence (released Mon. Sept 10; Sections 1.3-1.5)
L2: Conditioning and Bayes' rule
L3: Independence
Problem Set 2 due on Tue Sept 18
Unit 3: Counting (released Mon. Sept 17; Section 1.6)
L4: Counting
Problem Set 3 due on Tue Sept 25
Unit 4: Discrete random variables (released Wed. Sept 19; Sections 2.1-2.7)
L5: Probability mass functions and expectations
L6: Variance; Conditioning on an event; Multiple r.v.'s
L7: Conditioning on a random variable; Independence of r.v.'s
Problem Set 4 due on Tue Oct 2
Exam 1 (Timed) : Covers material from L1 to L7 (released Wed. Oct 3; due on Tue. Oct 9)
Unit 5: Continuous random variables (released Mon. Oct 1; Sections 3.1-3.5)
L8: Probability density functions
L9: Conditioning on an event; Multiple r.v.'s
L10: Conditioning on a random variable; Independence; Bayes' rule
Problem Set 5 due on Tue. Oct 16
Unit 6: Further topics on random variables (released Mon. Oct 15; Sections 4.1-4.3, 4.5)
L11: Derived distributions
L12: Sums of r.v.'s; Covariance and correlation
L13: Conditional expectation and variance revisited; Sum of a random number of r.v.'s
Problem Set 6 due on Tue. Oct 23
Unit 7: Bayesian inference (released Mon. Oct 22 Sections 3.6, 8.1-8.4)
L14: Introduction to Bayesian inference
L15: Linear models with normal noise
L16: Least mean squares (LMS) estimation
L17: Linear least mean squares (LLMS) estimation
Problem Set 7a due on Tue. Oct 30
Problem Set 7b due on Tue. Nov 6
Exam 2 (Timed): Covers material from L8 to L17 (released Wed. Nov 1; due on Nov 13)
Unit 8: Limit theorems and classical statistics (released Mon. Nov 5; Sections 5.1-5.4, pp. 466-475)
L18: Inequalities, convergence, and the Weak Law of Large Numbers
L19: The Central Limit Theorem (CLT)
L20: An introduction to classical statistics
Problem Set 8 due on Tue. Nov 27
Unit 9: Bernoulli and Poisson processes (released Tue. Nov 14; Sections 6.1-6-2)
L21: The Bernoulli process
L22: The Poisson process
L23: More on the Poisson process
Problem Set 9 due on Tue. Dec 4
Unit 10: Markov chains (released Tue. Nov 26; Sections 7.1-7-4)
L24: Finite-state Markov chains
L25: Steady-state behavior of Markov chains
L26: Absorption probabilities and expected time to absorption
Problem Set 10 due on Tue. Dec 11
Final Exam (Timed) (released Wed. Dec 12; due on Sun. Dec 23)
*Note: Problem set and exam due dates are at the end of the specified date, at 23:59 UTC.