Course  Probabilistic Systems Analysis and Applied Probability
Welcome to probabilistic systems analysis and applied probability, a subject on the modeling and analysis of random phenomena and processes, including the basics of statistical inference. Nowadays, there is broad consensus that the ability to think probabilistically is a fundamental component of scientific literacy. For example: 1)The concept of statistical significance (to be touched upon at the end of this course) is considered by the Financial Times as one of "The Ten Things Everyone Should Know About Science".2) A recent Scientific American article argues that statistical literacy is crucial in making healthrelated decisions.3) Finally, an article in the New York Times identifies statistical data analysis as an upcoming profession, valuable everywhere, from Google and Netflix to the Office of Management and Budget. The aim of this class is to introduce the relevant models, skills, and tools, by combining mathematics with conceptual understanding and intuition.

Lecture 1  Probability Models and Axioms

Lecture 2  Conditioning and Bayes' Rule

Lecture 3  Independence

Lecture 4  Counting

Lecture 5  Discrete Random Variables I

Lecture 6  Discrete Random Variables II

Lecture 7  Discrete Random Variables III

Lecture 8  Continuous Random Variables

Lecture 9  Multiple Continuous Random Variables

Lecture 10  Continuous Bayes' Rule; Derived Distributions

Lecture 11  Derived Distributions (ctd.); Covariance

Lecture 12  Iterated Expectations

Lecture 13  Bernoulli Process

Lecture 14  Poisson Process I

Lecture 15  Poisson Process II

Lecture 16  Markov Chains I

Lecture 17  Markov Chains II

Lecture 18  Markov Chains III

Lecture 19  Weak Law of Large Numbers

Lecture 20  Central Limit Theorem

Lecture 21  Bayesian Statistical Inference I

Lecture 22  Bayesian Statistical Inference II

Lecture 23  Classical Statistical Inference I

Lecture 24  Classical Inference II

Lecture 25  Classical Inference III