Course6.041SC149 lectures
Probabilistic Systems Analysis and Applied Probability
Prof. John Tsitsiklis · Massachusetts Institute of Technology
About
This course introduces students to the modeling, quantification, and analysis of uncertainty. The tools of probability theory, and of the related field of statistical inference, are the keys for being able to analyze and make sense of data. These tools underlie important advances in many fields, from the basic sciences to engineering and management.
Course Format
This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:
Lecture Videos by MIT Professor John Tsitsiklis
Lecture Slides and Readings
Recitation Problems and Solutions
Recitation Help Videos by MIT Teaching Assistants
Tutorial Problems and Solutions
Tutorial Help Videos by MIT Teaching Assistants
Problem Sets with Solutions
Exams with Solutions
Related Resource
Lectures
Lecture 1: Probability Models and Axioms
- Lecture 1: Probability Models and Axioms Video
- The Probability of the Difference of Two Events
- Geniuses and Chocolates
- Uniform Probabilities on a Square
Lecture 2: Conditioning and Bayes' Rule
- Lecture 2: Conditioning and Bayes' Rule Video
- A Coin Tossing Puzzle
- Conditional Probability Example
- The Monty Hall Problem
Lecture 3: Independence
- Lecture 3: Independence Video
- A Random Walker
- Communication over a Noisy Channel
- Network Reliability
- A Chess Tournament Problem
Lecture 4: Counting
Lecture 5: Discrete Random Variables; Probability Mass Functions; Expectations
- Lecture 5: Discrete Random Variables; Probability Mass Functions; Expectations Video
- Sampling People on Buses
- PMF of a Function of a Random Variable
Lecture 6: Discrete Random Variable Examples; Joint PMFs
- Lecture 6: Discrete Random Variable Examples; Joint PMFs Video
- Flipping a Coin a Random Number of Times
- Joint Probability Mass Function (PMF) Drill 1
- The Coupon Collector Problem
Lecture 7: Multiple Discrete Random Variables
Lecture 8: Continuous Random Variables
- Lecture 8: Continuous Random Variables Video
- Calculating a Cumulative Distribution Function (CDF)
- A Mixed Distribution Example
- Mean and Variance of the Exponential
- Normal Probability Calculation
Lecture 9: Multiple Continuous Random Variables
- Lecture 9: Multiple Continuous Random Variables Video
- Uniform Probabilities on a Triangle
- Probability that Three Pieces Form a Triangle
- The Absent Minded Professor
Lecture 10: Continuous Bayes' Rule; Derived Distributions
- Lecture 10: Continuous Bayes' Rule; Derived Distributions Video
- Inferring a Discrete Random Variable from a Continuous Measurement
- Inferring a Continuous Random Variable from a Discrete Measurement
- A Derived Distribution Example
- Ambulance Travel Time
Lecture 11: Derived Distributions; Convolution; Covariance and Correlation
- Lecture 11: Derived Distributions; Convolution; Covariance and Correlation Video
- The Difference of Two Independent Exponential Random Variables
- The Sum of Discrete and Continuous Random Variables
Lecture 12: Iterated Expectations; Sum of a Random Number of Random Variables
- Lecture 12: Iterated Expectations; Sum of a Random Number of Random Variables Video
- The Variance in the Stick Breaking Problem
- Widgets and Crates
- Using the Conditional Expectation and Variance
- A Random Number of Coin Flips
- A Coin with Random Bias
Lecture 13: Bernoulli Process
Lecture 14: Poisson Process - I
Lecture 15: Poisson Process - II
Lecture 16: Markov Chains - I
Lecture 17: Markov Chains - II
Lecture 18: Markov Chains - III
Lecture 19: Weak Law of Large Numbers
- Lecture 19 Video
- Convergence in Probability and in the Mean Part 1
- Convergence in Probability and in the Mean Part 2
- Convergence in Probability Example
Lecture 20: Central Limit Theorem
Lecture 21: Bayesian Statistical Inference - I
Lecture 22: Bayesian Statistical Inference - II
- Lecture 22 Video
- Inferring a Parameter of Uniform Part 1
- Inferring a Parameter of Uniform Part 2
- An Inference Example
Lecture 23 Classical Statistical Inference - I
Lecture 24: Classical Inference - II
Lecture 25: Classical Inference - III
Resource Index
- Lecture 1: Probability Models and Axioms1
- The Probability of the Difference of Two Events
- Geniuses and Chocolates
- Uniform Probabilities on a Square
- Lecture 2: Conditioning and Bayes' Rule2
- A Coin Tossing Puzzle
- Conditional Probability Example
- The Monty Hall Problem
- Lecture 3: Independence
- A Random Walker
- Communication over a Noisy Channel
- Network Reliability
- A Chess Tournament Problem
- Lecture 4: Counting
- Rooks on a Chessboard
- Hypergeometric Probabilities
- Lecture 5: Discrete Random Variables Probability Mass Functions Expectations
- Sampling People on Buses
- PMF of a Function of a Random Variable
- Lecture 6: Discrete Random Variable Examples Joint PMFs
- Flipping a Coin a Random Number of Times
- Joint Probability Mass Function (PMF) Drill 1
- The Coupon Collector Problem
- Lecture 7: Multiple Discrete Random Variables
- Joint Probability Mass Function (PMF) Drill 2
- Lecture 8: Continuous Random Variables
- Calculating a Cumulative Distribution Function (CDF)
- A Mixed Distribution Example
- Mean and Variance of the Exponential
- Normal Probability Calculation
- Lecture 9: Multiple continuous Random Variables
- Uniform Probabilities on a Triangle
- Probability that Three Pieces Form a Triangle
- The Absent Minded Professor
- Lecture 10: Continuous Bayes' Rule Derived Distributions
- Inferring a Discrete Random Variable from a Continuous Measurement
- A Derived Distribution Example
- Ambulance Travel Time
- Lecture 11: Derived Distributions Convolution Covariance and Correlation
- The Difference of Two Independent Exponential Random Variables
- The Sum of Discrete and Continuous Random Variables
- Lecture 12: Iterated Expectations Sum of a Random Number of Random variables
- The Variance in the Stick Breaking Problem
- Widgets and Crates
- Using the Conditional Expectation and Variance
- A Random Number of Coin Flips
- A Coin with Random Bias
- Lecture 13: Bernoulli Process
- Bernoulli Process Practice
- Lecture 14: Poisson Process - I
- Competing Exponentials
- Lecture 15: Poisson Process - II
- Random Incidence Under Erlang Arrivals
- Lecture 16: Markov Chains - I
- Setting Up a Markov Chain
- Markov Chain Practice 1
- Lecture 17: Markov Chains - II
- Lecture 18: Markov Chains - III
- Mean First Passage and Recurrence Times
- Lecture 19: Weak Law of Large Numbers
- Convergence in Probability and in the Mean Part 1
- Convergence in Probability and in the Mean Part 2
- Convergence in Probability Example
- Lecture 20: Central Limit Theorem
- Probabilty Bounds
- Using the Central Limit Theorem
- Lecture 21: Bayesian Statistical Inference - I
- Lecture 22: Bayesian Statistical Inference - II
- Inferring a Parameter of Uniform Part 1
- Inferring a Parameter of Uniform Part 2
- An Inference Example
- Lecture 23 Classical Statistical Inference - I
- Lecture 24: Classical Inference - II
- Lecture 25: Classical Inference - III Course Review
Syllabus and materials
At MIT OpenCourseWare, as the course publishes them.
Credits and licence
- Institution
- Massachusetts Institute of Technology
- Department
- Electrical Engineering and Computer Science
- Teacher
- Prof. John Tsitsiklis
- Term
- Fall 2013
- Level
- Undergraduate
- Language
- English
- Subjects
- Mathematics, Computer science, Engineering
- Source
- MIT OpenCourseWare
- Licence
- CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only. MIT OpenCourseWare's terms
- Attribution
- Prof. John Tsitsiklis. Probabilistic Systems Analysis and Applied Probability. Fall 2013. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.
- Who can watch
- MIT OpenCourseWare gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
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