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

• 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.