Build foundational knowledge of data science with this introduction to probabilistic models.
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Build foundational knowledge of data science with this introduction to probabilistic models.
--Course introduction, objectives, and study guide
--Syllabus, calendar, and grading policy
--Discussion forum and collaboration guidelines
--Homework mechanics and standard notation
--Lec. 1: Probability models and axioms
--Lec. 2: Conditioning and Bayes' rule
--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
--Additional theoretical material
-- 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
--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 ra
-- Additional theoretical material
--Lec. 14: Introduction to Bayesian inference
--Lec. 15: Linear models with normal noise
--Lec. 16: Least mean squares (LMS) estimation
--Lec. 17: Linear least mean squares (LLMS) estimation
--Additional theoretical material
--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
--Additional theoretical material
-- Lec. 21: The Bernoulli process
-- Lec. 22: The Poisson process
-- Lec. 23: More on the Poisson process
--Additional theoretical material
--Lec. 24: Finite-state Markov chains
--Lec. 25: Steady-state behavior of Markov chains
--Lec. 26: Absorption probabilities and expected time to absorption
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