Lecture 10: Continuous Bayes' Rule; Derived Distributions
Lecture 10: Continuous Bayes' Rule; Derived Distributions
Description: In this lecture, the professor discussed Bayes rule, Bayes variations, and derived distributions. Instructor: John Tsitsiklis
Lecture 11: Derived Distributions; Convolution; Covariance ...
Lecture 11: Derived Distributions; Convolution; Covariance and Correlation
Description: In this lecture, the professor discussed derived distributions, convolution, covariance and correlation. Instructor: John Tsitsiklis
Lecture 12: Iterated Expectations; Sum of a Random Number ...
Lecture 12: Iterated Expectations; Sum of a Random Number of Random ...
Description: In this lecture, the professor discussed conditional expectation and sum of a random number of random variables. Instructor: John Tsitsiklis
Lecture 13: Bernoulli Process
Lecture 13: Bernoulli Process
Description: In this lecture, the professor discussed Bernoulli process, random processes, basic properties of Bernoulli process, distribution of interarrival times, the time of the kth success, merging and splitting. Instructor: John Tsitsiklis
Lecture 14: Poisson Process I
Lecture 14: Poisson Process I
Description: In this lecture, the professor discussed Poisson process, distribution of number of arrivals, and distribution of interarrival times. Instructor: John Tsitsiklis
Lecture 15: Poisson Process II
Lecture 15: Poisson Process II
Description: In this lecture, the professor discussed Poisson process, merging, splitting, and random incidence. Instructor: John Tsitsiklis
Lecture 16: Markov Chains I
Lecture 16: Markov Chains I
Description: In this lecture, the professor discussed Markov process definition, n-step transition probabilities, and classification of states. Instructor: John Tsitsiklis
Lecture 17: Markov Chains II
Lecture 17: Markov Chains II
Description: In this lecture, the professor discussed Markov process, steady-state behavior, and birth-death processes. Instructor: John Tsitsiklis
Lecture 18: Markov Chains III
Lecture 18: Markov Chains III
Description: In this lecture, the professor discussed Markov Processes, probability of blocked phone calls, absorption probabilities, and calculating expected time to absorption. Instructor: John Tsitsiklis
Lecture 19: Weak Law of Large Numbers
Lecture 19: Weak Law of Large Numbers
Description: In this lecture, the professor discussed limit theorems, Chebyshev's inequality, and convergence "in probability". Instructor: John Tsitsiklis
Lecture 1: Probability Models and Axioms
Lecture 1: Probability Models and Axioms
Description: In this lecture, the professor discussed probability as a mathematical framework, probabilistic models, axioms of probability, and gave some simple examples. Instructor: John Tsitsiklis
Lecture 20: Central Limit Theorem
Lecture 20: Central Limit Theorem
Description: In this lecture, the professor discussed central limit theorem, Normal approximation, 1/2 correction for binomial approximation, and De Moivre–Laplace central limit theorem. Instructor: John Tsitsiklis
Lecture 21: Bayesian Statistical Inference I
Lecture 21: Bayesian Statistical Inference I
Description: In this lecture, the professor discussed Bayesian statistical inference and inference models. Instructor: John Tsitsiklis Note: The first few minutes of this video are missing.
Lecture 22: Bayesian Statistical Inference II
Lecture 22: Bayesian Statistical Inference II
Description: In this lecture, the professor discussed Bayesian statistical inference, least means squares, and linear LMS estimation. Instructor: John Tsitsiklis
Lecture 23: Classical Statistical Inference I
Lecture 23: Classical Statistical Inference I
Description: In this lecture, the professor discussed classical statistics, maximum likelihood (ML) estimation, and confidence intervals. Instructor: John Tsitsiklis
Lecture 24: Classical Inference II
Lecture 24: Classical Inference II
Description: In this lecture, the professor discussed classical inference, Linear regression, and binary hypothesis testing. Instructor: John Tsitsiklis
Lecture 25: Classical Inference III; Course Overview
Lecture 25: Classical Inference III; Course Overview
Description: In this lecture, the professor discussed classical inference, simple binary hypothesis testing, and composite hypotheses testing. Instructor: John Tsitsiklis
Lecture 2: Conditioning and Bayes' Rule
Lecture 2: Conditioning and Bayes' Rule
Description: In this lecture, the professor discussed conditional probability, multiplication rule, total probability theorem, and Bayes' rule. Instructor: John Tsitsiklis
Lecture 3: Independence
Lecture 3: Independence
Description: In this lecture, the professor discussed independence of two events, independence of a collection of events, and independence vs. pairwise independence. Instructor: John Tsitsiklis