# 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.

##### 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