Probability and Statistics with R


  • Basic Information

    • Instructor : Siva Athreya.
    • Email : athreya@isibang.ac.in or athreya@cmi.ac.i
    • Classes : Wednesday and Friday : 9:10-10:25
    • Scoring : Final Exam: 40%, Midterm Exam: 20%, Quizzes: 25%, In-class Worksheets and Homework: 15%.
    • Program : Msc. Data Science, Chennai Mathematical Institute.
    • Submission Platform: Moodle.

  • References


  • Week 1 : September 22nd and 24th


  • Week 2 : September 29th and October 1st

    • R-Computing Binomial Probabilities, Functions in R
    • Sample Space, Events, Probability
    • Equally likely Outcomes
    • Conditional Probability
    • Bayes Theorem
  • Readings:-
    • Chapter1 in Probability and Statistics with Examples using R by Siva Athreya, Deepayan Sarkar, and Steve Tanner.

  • Week 3 : October 6th and October 8th, 2021

    • Discrete Random Variables
    • Expectation and Variance
    • De Moivre's Binomial Central Limit Theorem
  • Readings:-
    • Chapter 4 in Probability and Statistics with Examples using R by Siva Athreya, Deepayan Sarkar, and Steve Tanner.

  • Week 4 : October 13th and October 15th, 2021

    • De Moivre's Binomial Central Limit Theorem
    • Poisson Approximation
    • Sampling with and without replacement
    • Probability Density Function
    • Continuous random variables
    • Uniform and Normal Distribution
  • Readings:-
    • Chapter 4 and Chapter 5 in Probability and Statistics with Examples using R by Siva Athreya, Deepayan Sarkar, and Steve Tanner.

  • Week 5 : October 20th and October 22nd, 2021

    • Probability on uncountable sample spaces.
    • Continuous Random Variables
    • Normal Random Variable and Exponential Random Variable
    • Distribution Function
  • Readings:-
    • Chapter 4 and Chapter 5 in Probability and Statistics with Examples using R by Siva Athreya, Deepayan Sarkar, and Steve Tanner.

  • Week 6 : October 27th and October 29th, 2021

    • Independence of Events and Random Variables
    • Joint Distribution and Conditional Distribution of Random Variables
    • Conditional Expectation and Variance
  • Readings:-
    • Chapter 1 and Chapter 3 in Probability and Statistics with Examples using R by Siva Athreya, Deepayan Sarkar, and Steve Tanner.

  • Week 7 : November 3rd, 2021

    • Covariance
    • Sums of Random Variables
  • Readings:-
    • Chapter 4 in Probability and Statistics with Examples using R by Siva Athreya, Deepayan Sarkar, and Steve Tanner.

  • Week 8 : November 10th and November 12th, 2021

  • Readings:-
    • Chapter 4 in Probability and Statistics with Examples using R by Siva Athreya, Deepayan Sarkar, and Steve Tanner.

  • Week 9 : November 16th, November 17th and November 19th, 2021


  • Week 10 : November 23rd, 24th, 26th 2021

    • Empirical Distribution
    • Unbiased and Consistent Estimate
    • Weak Law of Large Numbers.
    • Strong Law of Large Numbers (Statement).
    • Simulating Random Variables.
  • Readings:-
    • Chapter7 and Chapter8 in Probability and Statistics with Examples using R by Siva Athreya, Deepayan Sarkar, and Steve Tanner.

  • Week 11 : November 30th, December 1, 3 2021

    • $t$-confidence interval when variance is not known.
    • Method of Moments Estimate.
    • Maximum Likelihood Estimator.
  • Readings:-




  • Week 12 : December 7th,8th, and 10th 2021

    • Maximum Likelihood Estimator.
    • Hypothesis Testing
    • $z$-test for means with variance known
    • $t$-test for means with variance unknown
  • Readings:-

  • Week 13 : December 14th, 15th, and 17th 2021

    • $z$-test for comparison of sample means
    • $\chi^2$-goodness of fit test.
  • Readings:-
    • Chapter 9 in Probability and Statistics with Examples using R by Siva Athreya, Deepayan Sarkar, and Steve Tanner.
Last Modified: December 17th, 2021. CMI Moodle page Teaching Page