Probabilistic Systems Analysis and Applied Probability (2013)

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

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

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

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

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

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

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

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

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.

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

In this lecture, the professor discussed Poisson process, merging, splitting, and random incidence.

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

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

In this lecture, the professor discussed multiple random variables: conditioning and independence.

In this lecture, the professor discussed Bayes rule, Bayes variations, and derived distributions.

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

In this lecture, the professor discussed conditional expectation and sum of a random number of random variables.

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

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

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

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

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

In this lecture, the professor discussed random variables, probability mass function, expectation, and variance.

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

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