Probability and Random Variables

Dive into a comprehensive course on probability theory and random variables, covering fundamental concepts from axiomatic definitions to advanced topics like characteristic functions. Explore combinatorial methods, conditional probability, and product spaces before delving into random variables, distribution functions, and multivariate distributions. Learn about expected values, moments, and functions of random variables through a series of lectures spanning 14 weeks. Progress from basic probability axioms to complex topics such as the Central Limit Theorem, Bernoulli processes, and Poisson processes, gaining a solid foundation in probability and statistics along the way.

Probability & Random Variables - Week 2 - Lecture 1 - Probability Spaces; Axioms and properties ...
Probability & Random Variables - Week 2 - Lecture 2 - Discrete&Continuous Prob. Laws, Conditional P..
Probability & Random Variables - Week 2 - Lecture 3 - Discrete&Continuous Prob. Laws, Conditional P..
Probability & Random Variables - Week 3 - Lecture 1 - Total Probability Theorem, Bayes's Rule.
Probability & Random Variables - Week 3 - Lecture 2 - Independence, Conditional Independence.
Probability & Random Variables - Week 3 - Lecture 3 - Independence, Conditional Independence.
Probability & Random Variables - Week 4 - Lecture 1 - Independent Trials, Counting.
Probability & Random Variables - Week 4 - Lecture 2 - Discrete Random Variables.
Probability & Random Variables - Week 4 - Lecture 3 - Discrete Random Variables.
Probability & Random Variables - Week 5 - Lecture 1 - Expectation and Variance.
Probability & Random Variables - Week 5 - Lecture 2 - Properties of Expectation&Variance, Joint PMFs.
Probability & Random Variables - Week 5 - Lecture 3 - Properties of Expectation&Variance, Joint PMFs.
Probability & Random Variables - Week 6 - Lecture 1 - Conditional PMFs.
Probability & Random Variables - Week 6 - Lecture 2 - Conditioning one random variable on another.
Probability & Random Variables - Week 6 - Lecture 3 - Conditional Expectation.
Probability & Random Variables - Week 7 - Lecture 1 - Iterated expectation, independence of rvs.
Probability & Random Variables - Week 7 - Lecture 2 - Independence of Random Variables.
Probability & Random Variables - Week 7 - Lecture 3 - Independence of Random Variables.
Probability & Random Variables - Week 8 - Lecture 1 - Continuous Random Variables.
Probability & Random Variables - Week 8 - Lecture 2 - Expectation & Cumulative Distribution Function.
Probability & Random Variables - Week 8 - Lecture 3 - Expectation & Cumulative Distribution Function.
Probability & Random Variables - Week 9 - Lecture 1 - The Gaussian CDF.
Probability & Random Variables - Week 9 - Lecture 2 - Conditional PDFs, Joint PDFs.
Probability & Random Variables - Week 9 - Lecture 3 - Conditional PDFs, Joint PDFs.
Probability & Random Variables - Week 10 - Lecture 1 - Conditioning a continuous rv on another.
Probability & Random Variables - Week 10 - Lecture 2 - Conditional PDFs, Continuous Bayes's Rule.
Probability & Random Variables - Week 10 - Lecture 3 - Conditional PDFs, Derived Distributions.
Probability & Random Variables - Week 11 - Lecture 1 - Derived Distributions.
Probability & Random Variables - Week 11 - Lecture 2 - Functions of Random Variables, Derived PDFs.
Probability & Random Variables - Week 11 - Lec. 3 - Sum of Independent rvs, Correlation & Covariance.
Probability & Random Variables - Week 12 - Lecture 1 - Applications of Covariance.
Probability & Random Variables - Week 12 - Lecture 2 - Transforms (Moment Generating Functions).
Probability & Random Variables - Week 12 - Lecture 3 - Transforms (Moment Generating Functions).
Probability & Random Variables - Week 13 - Lec. 1-Markov&Chebychev Inequalities,Convergence In Prob..
Probability & Random Variables - Week 13 - Lecture 2 - The Weak Law of Large Numbers.
Probability & Random Variables - Week 13 - Lecture 3 [Part 1] - The Central Limit Theorem.
Probability & Random Variables - Week 13 - Lecture 3 [Part 2] - The Central Limit Theorem.
Probability & Random Variables - Week 14 - Lecture 1 - The Bernoulli Process.
Probability & Random Variables - Week 14 - Lecture 2 - The Poisson Process.
Probability & Random Variables - Week 14 - Lecture 3 - The Poisson Process.