Lec 1: Probability Models and Axioms
Lec 2: Conditioning and Bayes' Rule
Lec 3: Independence
Lec 4: Counting
Lec 5: Discrete Random Variables I
Lec 6: Discrete Random Variables II
Lec 7: Discrete Random Variables III
Lec 8: Continuous Random Variables
Lec 9: Multiple Continuous Random Variables
Lec 10: Continuous Bayes' Rule; Derived Distributions
Lec 11: Derived Distributions (ctd.); Covariance
Lec 12: Iterated Expectations
Lec 13: Bernoulli Process
Lec 14: Poisson Process I
Lec 15: Poisson Process II
Lec 16: Markov Chains I
Lec 17: Markov Chains II
Lec 18: Markov Chains III
Lec 19: Weak Law of Large Numbers
Lec 20: Central Limit Theorem
Lec 21: Bayesian Statistical Inference I
Lec 22: Bayesian Statistical Inference II
Lec 23: Classical Statistical Inference I
Lec 24; Classical Inference II
Lec 25: Classical Inference III
The proofs of these properties are both interesting and insightful. They illustrate the power of the third axiom, and its interaction with the remaining two axioms. When studying axiomatic probability theory, many deep consequences follow from merely these three axioms. In order to verify the monotonicity property, we set 
and 
, where 
for 
. It is easy to see that the sets 
are pairwise disjoint and 
. Hence, we obtain from the third axiom that 
John N. Tsitsiklis is a Clarence J Lebel Professor of Electrical Engineering,
with the Department of Electrical Engineering and Computer Science (EECS) at MIT.
Also affiliated with: :
Laboratory for Information and Decision Systems (LIDS)
Institute for Data, Systems, and Society (IDSS)
where he is serving as Graduate Officer and Head of the doctoral program on Social and Engineering Systems (SES)
Statistics and Data Science Center (SDSC)
Operations Research Center (ORC)
Teaching classes mostly on stochastic systems and optimization, including an EdX MOOC on Introduction to Probability, most likely to be offered again in Spring 2017
Fall 2016: 6.251/15.081 Introduction to Mathematical Programming Spring 2017: 6.231, Dynamic Programming and Stochastic Control
Research on systems, stochastic modeling, inference, optimization, control, etc.
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