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Probabilistic Systems Analysis and Applied Probability

Applied Probability of the System

COURSE
0
Students Enrolled : 0
Total lectures : 25

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

  • 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

 john tsitsiklis (mit)
Course: 0
Students: 0

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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