STAT 333 W19 Notes

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• Lecture 1(pdf) - January 8

  • Fundamental of Probability
    • Probability Models
    • Conditional Probability

• Lecture 2(pdf) - January 10

  • Fundamental of Probability(cont'd)
    • Independence
    • Bayes' rule
  • Random variables and distributions
    • Discrete random variables and distribution
      • Bernoulli distribution
      • Binomial distribution
      • Geometric distribution

• Lecture 3(pdf) - January 15

  • Random variables and distributions (cont'd)
    • Discrete random variables and distribution (cont'd)
      • Geometric distribution
      • Poisson distribution
    • Continuous random variables and distributions
      • Exponential distribution
    • Joint distribution
    • Expectation

• Lecture 4(pdf) - January 17

  • Random variables and distributions (cont'd)
    • Expectation (cont'd)
      • Properties of expectation
    • Indicator

• Lecture 5(pdf) - January 22

  • Random variables and distributions (cont'd)
    • Indicator (cont'd)
    • Moment generating function (mgf)
      • Joint mgf

• Lecture 6(pdf) - January 24

  • Conditional distribution and conditional expectation
    • Conditional distribution
    • Conditional expectation

• Lecture 7(pdf) - January 29

  • Conditional distribution and conditional expectation (cont'd)
    • Conditional expectation (cont'd)
    • Decomposition of variance (Conditional variance)

• Lecture 8(pdf) - January 31

  • 4. Stochastic Processes
    • Simple random walk

• Lecture 9(pdf) - February 05

  • 4. Stochastic Processes (cont'd)
    • Markov Chain
    • One-step transition probability matrix

• Lecture 10(pdf) - February 07

  • 4. Stochastic Processes (cont'd)
    • Chapman-Kolmogorov equations
    • Stationary distribution (invariant distribution)

• Lecture 11(pdf) - February 14

  • 4. Stochastic Processes (cont'd)
    • Stationary distribution (invariant distribution)(cont'd)
    • Classification of States
      • Transience and recurrence

• Lecture 12(pdf) - February 26

  • 4. Stochastic Processes (cont'd)
    • Stationary distribution (invariant distribution)(cont'd)
    • Classification of States
      • Periodicity
      • Equivalent classes and irreducibility
        • Assessable
        • Communicate
        • Class
        • Irreducible

• Lecture 13(pdf) - February 28

  • 4. Stochastic Processes (cont'd)
    • Stationary distribution (invariant distribution)(cont'd)
    • Classification of States
      • Periodicity
      • Equivalent classes and irreducibility
        • Proposition
      • Limiting Distribution
        • Basic Limit Theorem

• Lecture 13(pdf) - February 28

  • 4. Stochastic Processes (cont'd)
    • Stationary distribution (invariant distribution)(cont'd)
    • Classification of States
      • Periodicity
      • Equivalent classes and irreducibility
        • Proposition
      • Limiting Distribution
        • Basic Limit Theorem

• Lecture 14(pdf) - March 05

  • 4. Stochastic Processes (cont'd)
    • Limiting Distribution
      • Examples
    • 4.6 Generating function and branching processes
      • Properties of generating function

• Lecture 15(pdf) - March 07

  • 4. Stochastic Processes (cont'd)
    • 4.6 Generating function and branching processes
      • Properties of generating function (cont'd)
      • 4.6.1. Branching Process
        • 4.6.1.1. Mean and variance
        • 4.6.1.2.Extinction Probability

• Lecture 16(pdf) - March 12

  • 4. Stochastic Processes (cont'd)
    • 4.6. Generating function and branching processes (cont'd)
      • 4.6.1. Branching Process (cont'd)
        • 4.6.1.2. Extinction Probability (cont'd)
  • 5. Poisson Processes
    • 5.1. Counting Process
    • 5.2. Definition of Poisson Process

• Lecture 17(pdf) - March 12

  • 5. Poisson Processes (cont'd)
    • 5.3. Properties of Poisson Processes
      • 5.3.1. Continuous-time Markov Property
        • 5.3.1.1. Independent Increments
        • 5.3.1.2. Poisson Increments
        • 5.3.1.3. Combining and Thining of Poisson Process

• Lecture 18(pdf) - March 19

  • 5. Poisson Processes (cont'd)
    • 5.3. Properties of Poisson Processes (cont'd)
      • 5.3.1. Continuous-time Markov Property (cont'd)
        • 5.3.1.3. Combining and Thinning of Poisson Process (cont'd)
        • 5.3.1.4 Order Statistics Property
  • 6. Continuous-Time Markov Chain
    • 6.1. Definitions and Structures
      • Definition 6.1.1. Continuous-time Stochastic Process

• Lecture 19(pdf) - March 21

  • 6. Continuous-Time Markov Chain
    • 6.1. Definitions and Structures
      • Definition 6.1.1. Continuous-time Stochastic Process
      • Example 6.1.1.1.