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 $E_1=A$ 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 $P(A)+P(B\backslash A)+\sum_{i=3}^\infty P(\varnothing)=P(B).$

Course Curriculum

Probability ModelsAvailable now

Lec 1: Probability Models and Axioms 51m 11s
Lec 2: Conditioning and Bayes' Rule 51m 11s
Lec 3: Independence 46m 30s
Lec 4: Counting 51m 34s
Lec 5: Discrete Random Variables I 50m 35s
Lec 6: Discrete Random Variables II 50m 53s
Lec 7: Discrete Random Variables III 50m 42s
Lec 8: Continuous Random Variables 50m 29s
Lec 9: Multiple Continuous Random Variables 50m 51s
Lec 10: Continuous Bayes' Rule; Derived Distributions 48m 53s
Lec 11: Derived Distributions (ctd.); Covariance 51m 55s
Lec 12: Iterated Expectations 47m 54s
Lec 13: Bernoulli Process 50m 58s
Lec 14: Poisson Process I 52m 44s
Lec 15: Poisson Process II 49m 28s
Lec 16: Markov Chains I 52m 6s
Lec 17: Markov Chains II 51m 25s
Lec 18: Markov Chains III 51m 50s
Lec 19: Weak Law of Large Numbers 50m 13s
Lec 20: Central Limit Theorem 51m 23s
Lec 21: Bayesian Statistical Inference I 48m 50s
Lec 22: Bayesian Statistical Inference II 52m 16s
Lec 23: Classical Statistical Inference I 49m 32s
Lec 24; Classical Inference II 51m 50s
Lec 25: Classical Inference III 52m 7s

About Tutor

Tutor: john tsitsiklis (mit)

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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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23 Questions

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  Anant Gaggar
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  Anant Gaggar
  2/07/14 Friday 10:20am
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Probabilistic Systems Analysis and Applied Probability