Probability Theory

Welcome to Probability Theory course home page. I am Siva Athreya the instructor for the course.

Schedule: Monday and Wednesday from 10 to 11:30.

Location: TIFR, Bangalore, Campus.

Syllabus:
Orientation, Combinatorial probability and urn models, Independence of events, Conditional probabilities.

Standard discrete distributions (uniform, binomial, Poisson, geometric, hypergeometric) and Univariate densities and distributions, standard univariate densities (normal, exponential, gamma, beta, chi-square, cauchy). Random variables, Distributions, Expectation, Variance and moments, probability generating functions and moment generating functions. Tchebychev's inequality

Independence of random variables, Joint and conditional distributions. Transformation of variables (assuming Jacobian formula). Distributions of sum, maxima, minima, order statistics, range etc. Borel Cantelli Lemma, Markov Inequality, Weak law of Large numbers.

Characteristic functions: properties, illustrations, inversion formula, continuity theorem. Elements of modes of convergence of random variables, and the strong law of large numbers. Central Limit Theorem for i.i.d. case with finite variance.

Finite State Markov Chains. Examples, Classification of States, Stationary Distribution.

References:
P. Billingsley, Probability and measure.
Y. S. Chow and H. Teicher, Probability theory. Independence, interchangeability, martingales.
S.R. Athreya and V.S.Sunder, Measure and Probability.
W. Feller, Introduction to Probability Theory and Its Applications, Vol 1 and 2.

Scoring:
Final Exam is worth 40 %, Midterm is worth 35 % and Homework(s) and Quiz(es) are worth 25 %.

  • Homework 1
  • Homework 2
  • Homework 3
  • Homework 4
  • Practice Midterm Solutions

  • Homework 5
  • Homework 6
  • Homework 7
  • Homework 8
  • Homework 9
    If you have any questions or comments about the class/webpage/or anything else you can visit me at
    Room A12 , Main building
    Stat-Math Unit
    Indian Statistical Institute
    Bangalore.

    I can be reached via email at: athreyaATisibang.ac.in


    http://www.isibang.ac.in/~athreya/Teaching/prob10
    [Teaching]