Basic Probability


  • Basic Information

    •
    • Instructor : Siva Athreya .
    • Email : athreya@isibang.ac.in
    • Classes : Tuesday and Thursday: 08:55-10:30
    • Syllabi :

      Orientation. Combinatorial probability. Fluctuations in Coin Tossing and Random Walks.Combination of Events, Occupancy and Matching Problems. Conditional probabilities. Urn Models. Independence.

      Random Variables, discrete distributions, Expectation, variance and moments, probability generating functions and moment generating functions, Tchebychevs inequality. Standard discrete distributions: uniform, binomial, Poisson, geometric, hypergeometric, negative binomial.

      Continuous random variables: univariate densities and distributions, Expectations, variance andmoments, standard univariate densities: normal, exponential, gamma, beta, chi-square, Cauchy.

      Joint and conditional distributions, Independence of random variables, Transformation of vari-ables.

      Laws of Large Numbers and Central Limit Theorem (Proofs optional)

    • Scoring : Take home Exam(s): 50%, Homework: 50%.

  • References


Videos:
During every class we shall watch a 5min video before class starts. Below is the selection of what we watched during the semester.

  • Pre-Week 1

    •
  • Comprehensive Assignment. (Please use this assignment to judge if you (already) have competency in course material that will be covered during the semester)
  • Topics Covered
    • Overview of course material.

  • Week 1 : September 1 and September3, 2020.

    •
  • Topics Covered
    • Zoom basics.
    • Moodle basics
    • Quiz submission

  • Week 2 : September 8 and September 10, 2020.

    •
  • Topics Covered
    • Sample Space, Events and Probability

  • Week 2 : September 15 and September 17, 2020.

    •
  • $17^\mbox{th}$-September Video:- Part I.
  • $15^\mbox{th}$-September: Notes.
  • $17^\mbox{th}$-September: Notes.
  • Topics Covered
    • Conditionaly Probability and Indpendence

  • Week 3 : September 22 and September 24, 2020.

    •
  • Topics Covered
    • Indpendence and Bernoulli Trials

  • Week 4 : September 29 and October 1, 2020.

    •
  • Topics Covered
    • Poisson Approximation
    • Sampling without Replacement
    • Discrete Random Variables

  • Week 5 : October 6 and 8 2020.

    •
  • Topics Covered
    • Distribution, Probability Mass function
    • Joint, Marginal, and Conditional
    • Independence

  • Week 6 : October 13 and 15, 2020.

    •
  • Topics Covered
  • Distribution of Functions of Random Variables
  • Expectation of Random Variables

  • Week 7 : October 20 and 22, 2020.

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  • $20^\mbox{th}$-October: Notes.
  • $22^\mbox{nd}$-October: Notes.
  • Topics Covered
    • Expectation and Variance

  • Week 8 : October 27 and 29, 2020.

    •
  • $27^\mbox{th}$-October: Notes.
  • $29^\mbox{th}$-October: Notes.
  • Topics Covered
    • Conditional Expectation, Conditional Variance
    • Continuous Random Variables: Uniform Distribution

  • Week 9 : November 3 and 5, 2020.

    •
  • $3^\mbox{rd}$-November: Notes.
  • $5^\mbox{th}$-November: Notes.
x
  • Topics Covered
    • Exponential, Normal Random Variable
    • Change of Variable

  • Week 10 : November 10 and 12, 2020.

    •
  • Topics Covered
    • Marginal Density
    • Joint Density
    • Conditional Density

  • Week 11 : November 17 and 19, 2020.

    •
  • Topics Covered
    • Sums of Random Variables
    • Quotients of Random Variables

  • Week 10 : November 24 and 26, 2020.

    •
  • Topics Covered
    • Law of Large numbers

  • Week 14 : December 1 and 3, 2020.

    •
  • Topics Covered
Last Modified: December 1, 2020. Courses Page Teaching Page