What will I learn from this course?
Thorough in Probabilistic Systems Analysis
Requirements
Any body who wants understand the Probabilistic Systems Analysis
Who is the target audience?
Any body who intrested in Probabilistic Systems Analysis
Description
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 
Course Curriculum
- Lec 1: Probability Models and Axioms 51m 11s Preview
- Lec 2: Conditioning and Bayes' Rule 51m 11s Preview
- Lec 3: Independence 46m 30s Preview
- Lec 4: Counting 51m 34s Preview
- Lec 5: Discrete Random Variables I 50m 35s Preview
- Lec 6: Discrete Random Variables II 50m 53s Preview
- Lec 7: Discrete Random Variables III 50m 42s Preview
- Lec 8: Continuous Random Variables 50m 29s Preview
- Lec 9: Multiple Continuous Random Variables 50m 51s Preview
- Lec 10: Continuous Bayes' Rule; Derived Distributions 48m 53s Preview
- Lec 11: Derived Distributions (ctd.); Covariance 51m 55s Preview
- Lec 12: Iterated Expectations 47m 54s Preview
- Lec 13: Bernoulli Process 50m 58s Preview
- Lec 14: Poisson Process I 52m 44s Preview
- Lec 15: Poisson Process II 49m 28s Preview
- Lec 16: Markov Chains I 52m 6s Preview
- Lec 17: Markov Chains II 51m 25s Preview
- Lec 18: Markov Chains III 51m 50s Preview
- Lec 19: Weak Law of Large Numbers 50m 13s Preview
- Lec 20: Central Limit Theorem 51m 23s Preview
- Lec 21: Bayesian Statistical Inference I 48m 50s Preview
- Lec 22: Bayesian Statistical Inference II 52m 16s Preview
- Lec 23: Classical Statistical Inference I 49m 32s Preview
- Lec 24; Classical Inference II 51m 50s Preview
- Lec 25: Classical Inference III 52m 7s Preview
About Tutor
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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