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Probabilistic Systems Analysis and Applied Probability

Applied Probability of the System Video Course By John Tsitsiklis (MIT)
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Students Enrolled: 0 Total Lecturs: 25
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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

Course Curriculum

Total: 25 lectures

  • 51m 11s

    Lec 1: Probability Models and Axioms

  • 51m 11s

    Lec 2: Conditioning and Bayes' Rule

  • 46m 30s

    Lec 3: Independence

  • 51m 34s

    Lec 4: Counting

  • 50m 35s

    Lec 5: Discrete Random Variables I

  • 50m 53s

    Lec 6: Discrete Random Variables II

  • 50m 42s

    Lec 7: Discrete Random Variables III

  • 50m 29s

    Lec 8: Continuous Random Variables

  • 50m 51s

    Lec 9: Multiple Continuous Random Variables

  • 48m 53s

    Lec 10: Continuous Bayes' Rule; Derived Distributions

  • 51m 55s

    Lec 11: Derived Distributions (ctd.); Covariance

  • 47m 54s

    Lec 12: Iterated Expectations

  • 50m 58s

    Lec 13: Bernoulli Process

  • 52m 44s

    Lec 14: Poisson Process I

  • 49m 28s

    Lec 15: Poisson Process II

  • 52m 6s

    Lec 16: Markov Chains I

  • 51m 25s

    Lec 17: Markov Chains II

  • 51m 50s

    Lec 18: Markov Chains III

  • 50m 13s

    Lec 19: Weak Law of Large Numbers

  • 51m 23s

    Lec 20: Central Limit Theorem

  • 48m 50s

    Lec 21: Bayesian Statistical Inference I

  • 52m 16s

    Lec 22: Bayesian Statistical Inference II

  • 49m 32s

    Lec 23: Classical Statistical Inference I

  • 51m 50s

    Lec 24; Classical Inference II

  • 52m 7s

    Lec 25: Classical Inference III

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 E_1=A and E_2=B\backslash A, where \quad A\subseteq B \text{ and } E_i=\varnothing for i\geq 3. It is easy to see that the sets E_i are pairwise disjoint and E_1\cup E_2\cup\ldots=B. Hence, we obtain from the third axiom that  P(A)+P(B\backslash A)+\sum_{i=3}^\infty P(\varnothing)=P(B).

About Tutor

  • Tutor: John Tsitsiklis (MIT)
  • Tests Packages: 0
  • Students: 0
4.4

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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