INDIAN STATISTICAL INSTITUTE (Delhi Centre) 7 S. J. S. Sansanwal Marg, New Delhi 110016

Instructor: Antar Bandyopadhyay (Email: antar (at) isid (dot) ac (dot) in Office: Room # 208 First Floor of Faculty Block, ISI, Delhi).

Class Time: Monday & Wednesday 12:10 PM - 1:30 PM at Room # 22, Academic Block, ISI, Delhi & Online/Hybrid in the other locations.

Tutorial Times: Tuesday 05:00 PM - 05:40 PM & Thursday 04:00 PM - 04:50 PM.

Lecture Hall: Room # 22 Academic Block (First Floor), ISI, Delhi and (via online/hybrid more) at the respective BSDS Classrooms in Kolkata & Bangalore.

Google Classroom for all announcements and other information purpose.

TAs:

• At ISI, Kolkata: Bishakh Bhattacharya, SRF, Statistics, TSMU, Kolkata (E-Mail: bishakh.rik (at) gmail (dot) com> ).
• At ISI, Delhi: Maruf Tarafdar, JRF, Statistics, TSMU, Delhi (E-Mail: tarafdarmaruf76 (at) gmail (dot) com> ).
• At ISI, Bangalore: Shubham Ovhal, SRF, Mathematics, TSMU, Bangalore (E-Mail: rs_math2104 (at) isibang (dot) ac (dot) in> ).

Course Duration: August 12, 2024 - November 29, 2024 (s total of 14 weeks classes for which 7 weeks will be prior to the midterm week and 7 weeks after).

Midterm Examination: Tuesday, October 01, 2024 during 10:30 AM - 12:30 PM

Final Examination: Wednesday, December 11, 2024 during 10:30 AM - 01:30 PM

Backpaper Examination: TBA(During the week of January 06 - 10, 2024)

For more details see Academic Calender for BSDS.

Course Outline:

• Mathematical set-up for probability, equally likely outcomes, basic counting arguments.
• Conditional probability, Bayes' rule, independent events.
• Sampling with and without replacement, Binomial distribution, Normal and Poisson approximations.
• Discrete random variables: Discrete Uniform, Bernoulli, Binomial, Poisson, Hypergeometric, Geometric distributions.
• Discrete joint and conditional distributions, independent random variables, repeated trials. Negative Binomial Distribution.
• Expectation of a random variable. Variance, standard error.
• Continuous random variables, density, cumulative distribution function, change of variable formula.
• Uniform, Exponential, Gamma, Beta and Normal distribution.
• Expectation, variance and functional transforms of continuous random variables.
• Continuous joint distributions, independence.
• Discrete and continuous conditional distributions and conditional expectations.
• Covariance and correlation of two random variables. Correlation and independence.
• Distribution of sums, products and quotients for continuous distributions, Student’s-t, Chi-square and F-distributions and their elementary properties.

Knowledge requirement: High School level calculus will be of serious need. We will need various summations formulas, inequalities, summation of infinite series, limits, differentiation, integration, integration of function of two variables.

Text : Jim Pitman - Probability.

Other References : Here are two more books which are good to look at for reading and problem solving. You may not want to buy them, best would be to borrow these from the library.

• R. G. Hoel, S. C. Port and C. J. Stone - Introduction to Probability Theory.
• Sheldon M. Ross - A First Course in Probability, 6th Edition.

Grading Policy:

• Assignments: 10% of the total credit.
• Quizzes: 10% of the total credit.
• Midterm Exam: 30% of the total credit.
• Final Exam: 50% of the total credit.

Assignment Policies:

• There will be a total of 14 sets of homework assignments each carrying a total of 10 points. The average of the 10 best assignment scores will be taken for the Assignment component of the final grading.
• The assignments will be uploaded in the Google Classroom on every Wednesday, starting from August 21, 2024. Each assignment will be due on the following Thursday in the tutorial. You need to submit your handwritten hard copy of your solution of the assignment to your TA in the class. For example the first assignment is due on Thursday, August 29, 2024.
• Each Assignment will be based on the course materials which will be covered in the class in the week of its assignment.
• Late submission of an assignment will NOT BE ACCEPTED. If you can not submit an assignment on time, don't worry about it and try to do well in the others. It will not count in your final grade since you have four extra assignments anyway.
• Assignments will be graded by the respective TAs at your own location and the graded assignments will be returned to you in the local tutorials.

Quiz Policies:

• There will be at least four quizzes as surprise tests given in the class. This means there shall be no pre-scheduling. A quiz will cover materials done in the lectures given in the weeks prior to it.
• Each quiz will be of 10 points and will be of 20 minutes duration.
• Final grade for the quizzes will be (Best Score Before Midterm + Best Score Between Midterm and Final)/2.
• There will be NO supplementary quiz given for any student who may miss a quiz for whatsoever reason. If you miss one then do not worry, try doing well in the others.
• All quizzes will be part of the final grading.
• All quizzes will be closed note and closed book examinations.

Exam Policies:

• The Midterm and the Final Examinations will be close notes, close book examinations. That means, students will NOT be allowed to bring his/her own hand written notes, study materials, list of theorems etc., any printed or photocopied materials including books and handouts.
• Any unfair means used by any students in the examinations will be dealt with the strictest possible measures, as per the Institute rules. In particular, if any student is found to be using any kind of unfair practice during any of the examinations (including the quizzes) then he/she will be awarded ZERO in that examination.

Regrading Policy:

• Regrading of homeworks or exams will only be undertaken in cases where, you believe there has been a genuine error or misunderstanding. Please note that our primary aim in grading is consistency, so that all students are treated the same; for this reason, we will not adjust the score of one student on an issue of partial credit, unless the score allocated clearly deviates from the grading policy we adopted for that problem.
• If you wish to request a regrading of a homework or exam, you must return it to the instructor with a written note on a separate piece of paper explaining the problem.
• The entire assignment or the exam may be regraded, so be sure to check the solutions to ensure that your overall score will go up after regrading.
• All such requests must be received within one week from the date on which the homework or exam was made available for return.

Last modified November 29, 2024.