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Introduction

Course on undergraduate-level probability and random process. Lectured by Prof. Yung Yi, KAIST, South Korea (19fall, 21fall).


Textbook

Introduction to Probability, 2nd edition by Dimitri P. Bertsekas and John N. Tsitsiklis

images/probcover-2nd.jpg

Lecture slide latex files

Download from Github. They have been made by Prof. Yung YI, using LaTex Beamer package in the overleaf editing platform. They will keep being updated (most recent update: 21feb). Feel free to download, modify, and use them. Some figures, examples, and texts are borrowed from the lecture slides of the MIT probability course.

Topics   Contents/Videos/Schedule  Materials  
0. Introduction (08/30)
  • Total Time: (29.17 mins, 0.5 week)
  1. Course logistics
  2. Why probability? [Youtube (10:24)]
  • Lecture slides
  • For prints: 1, 2, 4
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    1. Probabilistic Model (09/01)
    • Total Time: (33.16 mins, 0.5 week)
    1. Probailistic model [Youtube (4:34)]
    2. Sample space, Event, and Probability Law [Youtube (7:01)]
    3. Probability axioms (1) [Youtube (6:27)]
    4. Probability axioms (2) [Youtube (15:14)]
  • Lecture slides
  • For prints: 1, 2, 4
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    2. Conditioning and Independence (09/06)
    • Total Time (48.2 mins, 0.5 week)
    1. Conditional Probability [Youtube] (10:56)
    2. Bayes' rule and Inference [Youtube] (19:47)
    3. Independence and Conditional Independence [Youtube] (17:37)
  • Lecture slides
  • For prints: 1, 2, 4
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    3. Random Variable, Part I (09/08, 09/13))
    • Total Time (82.65 mins, 1.5 week)
    1. Random Variable: Idea and Definition [Youtube] (7:57)
    2. Popular Discrete Random Varaibles: Bernoulli, Uniform, Binomial, Geometric, Poisson [Youtube] (8:42)
    3. Summarizing RVs: Expectation and Variance [Youtube] (11:09)
    4. Functions of Multiple Random Variables: Joint PMF, Marginal PMF [Youtube] (8:20)
    5. Conditioning for Random Variables [Youtube] (27:17)
    6. Independence for Random Variables [Youtube] (19:14)
  • Lecture slides
  • For prints: 1, 2, 4
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    4. Random Variable, Part II (09/15, 09/20, 09/22)
    • Total Time (115.8 mins, 1.5 week)
    1. Continuous Random Variable and PDF (Probability Density Function) [Youtube] (5:51)
    2. CDF (Cumulative Distribution Function) [Youtube] (9:36)
    3. Exponential RVs [Youtube] (23:00)
    4. Gaussian (Normal) RVs [Youtube] (11:13)
    5. Continuous RVs: Joint, Conditioning, and Independence [Youtube] (30:14)
    6. Bayes' Rule for RVs [Youtube] (21:00)
    7. Example: Buffon's Needle [Youtube] (15:42)
  • Lecture slides
  • For prints: 1, 2, 4
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    5. Random Variable, Part III (09/27, 09/29)
    • Total Time (108.65 mins, 1.5 week)
    1. Derived Distribution of Y=g(X) or Z=g(X,Y) [Youtube] (21:38)
    2. Derived Distribution of Z=X+Y [Youtube] (17:21)
    3. Covariance: Degree of Dependence between Two RVs [Youtube] (19:43)
    4. Correlation Coefficient [Youtube] (10:29)
    5. Conditional Expectation and Law of Iterative Expectations [Youtube] (20:57)
    6. Conditional Variance and Law of Total Variance [Youtube] (14:06)
    7. Random Number of Sum of RVs [Youtube] (4:25)
  • Lecture slides
  • For prints: 1, 2, 4
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    6. Limit of Scaled Sum of Random Variables (10/06, 10/11, 10/13)
    • Total Time (132.6 mins, 1.5 week)
    1. Weak Law of Large Numbers: Result and Meaning [Youtube] (34:23)
    2. Central Limit Theorem: Result and Meaning [Youtube] (34:28)
    3. Weak Law of Large Numbers: Proof, Inequalities (Markov and Chebyshev) [Youtube] (15:46)
    4. Comparison:Weak Law of Large Numbers and Central Limit Theorem [Youtube] (12:15)
    5. Central Limit Theorem: Proof, Moment Generating Function (MGF) [Youtube] (35:44)
  • Lecture slides
  • For prints: 1, 2, 4
    		•

    Mid-term Exam

    • Date: TBA, Location: TBA
    7. Random Process, Part I:
    Bernoulli and Poisson Process (10/25, 10/27, 11/01, 11/03)
    • Total Time (247.90 mins, 2 week)
    1. Introduction of Random Processes [Youtube] (24:40)
    2. Bernoulli Processes: Concepts and Basic Questions [Youtube] (10:40)
    3. Bernoulli Processes: Memorylessness and Fresh Restart [Youtube] (25:06)
    4. Bernoulli Processes: Busy Periods and Time of k-th arrival (Pascal RV) [Youtube] (24:19)
    5. Poisson Processes: Poisson RV and Cotinuous Twin of Bernoulli Process [Youtube] (36:08)
    6. Poisson Processes: Definition and Properties [Youtube] (25:34)
    7. Poisson Processes: Examples [Youtube] (10:55)
    8. Interarrival Time View, Coding, and Split and Merge of Bernoulli Process [Youtube] (19:23)
    9. Split and Merge of Proisson Process [Youtube] (17:41)
    10. Example Applications of Split and Merging of Bernulli and Poisson Processes [Youtube] (32:19)
    11. Random Incidence [Youtube] (21:15)
  • Lecture slides
  • For prints: 1, 2, 4
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    8. Random Process, Part II:
    Markov Chain (11/08, 11/10, 11/15, 11/17)
    • Total Time (198.9 mins, 2 week)
    1. Definition, Transition Probability Matrix, State Transition Diagram [Youtube] (24:06)
    2. Markov Chain: Examples [Youtube] (22:16)
    3. n-step Transition Probability [Youtube] (26:35)
    4. Classification of States [Youtube] (34:31)
    5. Steady-state Behaviors: Concept [Youtube] (26:42)
    6. Stationary Distribution and Steady-state Examples [Youtube] (12:41)
    7. Birth-Death Process: Examples and Concept [Youtube] (22:16)
    8. Transient Behaviors [Youtube] (29:49)
    9. BP, PP, and MC: How They Are Related (To Be Added)
  • Lecture slides
  • For prints: 1, 2, 4
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    9. Introduction to Statistical Inference (11/22, 11/24, 11/29, 12/01)
    • Total Time (218.85 mins, 2 week)
    1. Overview on Statistical Inference [Youtube] (33:09)
    2. Bayesian Inference: Framework [Youtube] (17:23)
    3. Bayesian Inference: Examples [Youtube] (39:05)
    4. MAP (Maximum A Posteriori) Estimator [Youtube] (34:47)
    5. LMS (Least Mean Squares) Estimator [Youtube] (32:47)
    6. LLMS (Linear LMS) Estimator [Youtube] (38:00)
    7. Classical Inference: ML Estimator [Youtube] (23:40)
  • Lecture slides
  • For prints: 1, 2, 4
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