MIT 6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013

This course introduces students to the modeling, quantification, and analysis of uncertainty. Created by MIT OpenCourseWare.


Average Course Length

32.5 hours


Skill Level

Intermediate



Pick a lesson


1: 1. Probability Models and Axioms
2: The Probability of the Difference of Two Events
3: Geniuses and Chocolates
4: Uniform Probabilities on a Square
5: 2. Conditioning and Bayes' Rule
6: A Coin Tossing Puzzle
7: Conditional Probability Example
8: The Monty Hall Problem
9: 3. Independence
10: A Random Walker
11: Communication over a Noisy Channel
12: Network Reliability
13: A Chess Tournament Problem
14: 4. Counting
15: Rooks on a Chessboard
16: Hypergeometric Probabilities
17: 5. Discrete Random Variables I
18: Sampling People on Buses
19: PMF of a Function of a Random Variable
20: 6. Discrete Random Variables II
21: Flipping a Coin a Random Number of Times
22: Joint Probability Mass Function (PMF) Drill 1
23: The Coupon Collector Problem
24: 7. Discrete Random Variables III
25: Joint Probability Mass Function (PMF) Drill 2
26: 8. Continuous Random Variables
27: Calculating a Cumulative Distribution Function (CDF)
28: A Mixed Distribution Example
29: Mean & Variance of the Exponential
30: Normal Probability Calculation
31: 9. Multiple Continuous Random Variables
32: Uniform Probabilities on a Triangle
33: Probability that Three Pieces Form a Triangle
34: The Absent Minded Professor
35: 10. Continuous Bayes' Rule; Derived Distributions
36: Inferring a Discrete Random Variable from a Continuous Measurement
37: Inferring a Continuous Random Variable from a Discrete Measurement
38: A Derived Distribution Example
39: The Probability Distribution Function (PDF) of [X]
40: Ambulance Travel Time
41: 11. Derived Distributions (ctd.); Covariance
42: The Difference of Two Independent Exponential Random Variables
43: The Sum of Discrete and Continuous Random Variables
44: 12. Iterated Expectations
45: The Variance in the Stick Breaking Problem
46: Widgets and Crates
47: Using the Conditional Expectation and Variance
48: A Random Number of Coin Flips
49: A Coin with Random Bias
50: 13. Bernoulli Process
51: Bernoulli Process Practice
52: 14. Poisson Process I
53: Competing Exponentials
54: 15. Poisson Process II
55: Random Incidence Under Erlang Arrivals
56: 16. Markov Chains I
57: Setting Up a Markov Chain
58: Markov Chain Practice 1
59: 17. Markov Chains II
60: 18. Markov Chains III
61: Mean First Passage and Recurrence Times
62: 19. Weak Law of Large Numbers
63: Convergence in Probability and in the Mean Part 1
64: Convergence in Probability and in the Mean Part 2
65: Convergence in Probability Example
66: 20. Central Limit Theorem
67: Probabilty Bounds
68: Using the Central Limit Theorem
69: 21. Bayesian Statistical Inference I
70: 22. Bayesian Statistical Inference II
71: Inferring a Parameter of Uniform Part 1
72: Inferring a Parameter of Uniform Part 2
73: An Inference Example
74: 23. Classical Statistical Inference I
75: 24. Classical Inference II
76: 25. Classical Inference III