# 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.

32.5 hours

###### Skill Level

Intermediate

Creative Commons (non commercial)

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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