Learn · Probabilistic Systems Analysis and Applied Probability
Lecture 123 of 149Resource Index51 min
Lecture 13: Bernoulli Process
Prof. John Tsitsiklis · Massachusetts Institute of Technology
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- Probabilistic Systems Analysis and Applied Probability, Massachusetts Institute of Technology (at MIT OpenCourseWare)
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- CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only.
- 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.
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All the lectures
- 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 Video
- A Coin Tossing Puzzle
- Conditional Probability Example
- The Monty Hall Problem
- Lecture 3: Independence Video
- A Random Walker
- Communication over a Noisy Channel
- Network Reliability
- A Chess Tournament Problem
- Lecture 4: Counting Video
- Rooks on a Chessboard
- Hypergeometric Probabilities
- 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 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 Video
- Joint Probability Mass Function (PMF) Drill 2
- 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 Video
- Uniform Probabilities on a Triangle
- Probability that Three Pieces Form a Triangle
- The Absent Minded Professor
- 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 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 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 Video
- Bernoulli Process Practice
- Lecture 14 Video
- Competing Exponentials
- Lecture 15 Video
- Random Incidence Under Erlang Arrivals
- Lecture 16 Video
- Setting Up a Markov Chain
- Markov Chain Practice 1
- Lecture 17 Video
- Lecture 18 Video
- Mean First Passage and Recurrence Times
- 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 Video
- Probabilty Bounds
- Using the Central Limit Theorem
- Lecture 21 Video
- Lecture 22 Video
- Inferring a Parameter of Uniform Part 1
- Inferring a Parameter of Uniform Part 2
- An Inference Example
- Lecture 23 Video
- Lecture 24 Video
- Lecture 25 Video
- 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