Probabilistic Systems Analysis and Applied Probability (Fall 2013)

Probabilistic Systems Analysis and Applied Probability (Fall 2013)

Prof. John Tsitsiklis via MIT OpenCourseWare Direct link

PMF of a Function of a Random Variable

19 of 76

19 of 76

PMF of a Function of a Random Variable

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Classroom Contents

Probabilistic Systems Analysis and Applied Probability (Fall 2013)

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

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