Probability that Three Pieces Form a Triangle

In this lecture, the professor discussed classical statistics, maximum likelihood (ML) estimation, and confidence intervals.

Lecture 23: Classical Statistical Inference I

In this lecture, the professor discussed classical inference, Linear regression, and binary hypothesis testing.

Lecture 24: Classical Inference II

In this lecture, the professor discussed Bayesian statistical inference, least means squares, and linear LMS estimation.

Lecture 22: Bayesian Statistical Inference II

In this lecture, the professor discussed Bayesian statistical inference and inference models.

Lecture 21: Bayesian Statistical Inference I

In this lecture, the professor discussed central limit theorem, Normal approximation, 1/2 correction for binomial approximation, and De Moivre–Laplace central limit theorem.

Lecture 20: Central Limit Theorem

In this lecture, the professor discussed classical inference, simple binary hypothesis testing, and composite hypotheses testing.

Lecture 25: Classical Inference III

In this lecture, the professor discussed Markov Processes, probability of blocked phone calls, absorption probabilities, and calculating expected time to absorption.

Lecture 18: Markov Chains III

In this lecture, the professor discussed limit theorems, Chebyshev's inequality, and convergence "in probability".

Lecture 19: Weak Law of Large Numbers

In this lecture, the professor discussed Markov process, steady-state behavior, and birth-death processes.

Lecture 17: Markov Chains II

Probabilistic Systems Analysis and Applied Probability (2013)

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.

Lecture 13: Bernoulli Process

In this lecture, the professor discussed Poisson process, distribution of number of arrivals, and distribution of interarrival times.

Lecture 14: Poisson Process I

In this lecture, the professor discussed Markov process definition, n-step transition probabilities, and classification of states.

Lecture 16: Markov Chains I

In this lecture, the professor discussed derived distributions, convolution, covariance and correlation.

Lecture 11: Derived Distributions (ctd

In this lecture, the professor discussed multiple random variables, expectations, and binomial distribution.

Lecture 7: Discrete Random Variables III

In this lecture, the professor discussed probability density functions, cumulative distribution functions, and normal random variables.

Lecture 8: Continuous Random Variables

In this lecture, the professor discussed conditional probability, multiplication rule, total probability theorem, and Bayes' rule.

Lecture 2: Conditioning and Bayes' Rule

In this lecture, the professor discussed independence of two events, independence of a collection of events, and independence vs. pairwise independence.

Lecture 3: Independence

In this lecture, the professor discussed principles of counting, permutations, combinations, partitions, and binomial probabilities.

Lecture 4: Counting

In this lecture, the professor discussed conditional PMF, geometric PMF, total expectation theorem, and joint PMF of two random variables.

Lecture 6: Discrete Random Variables II

In this lecture, the professor discussed probability as a mathematical framework, probabilistic models, axioms of probability, and gave some simple examples.

Lecture 1: Probability Models and Axioms

Rooks on a Chessboard

Uniform Probabilities on a Triangle

The Probability Distribution Function (PDF) of [X]

Using the Central Limit Theorem

Setting Up a Markov Chain

PMF of a Function of a Random Variable

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