July, 2019

A first undergraduate course in probability and statistics with a focus on discrete spaces. The course is roughly divided in to 4 equal parts with an exam at the end of each part.

Assignment Test: 20%

- Practice problems are given at the end of each lecture.
- There will be 2, 30 min tests per quarter (8 in total), based on the practice problems as well as OCW Recitations.
- Tests will be for 3 marks each and the scores of best 6 out 8 will be used for grading.
- 2 marks is allocated for solving some tricky problems that will be shared.

Quiz 1, Quiz 2: 10% each

MidSem: 25%

EndSem: 35%

Bonus Marks: 5% (For questions based on Bonus Topics).

*Attend*all the lectures (90 mins each).*Read*the corresponding topics in the textbook on the same day (1 hr after each lecture).*Solve*the problems for the previous lecture before the next lecture (2 hr after each lecture).*Ask*doubts and clear them during tutorials (60 mins).*Explore*bonus topics for fun and get bonus points.

So weekly there is 4 hrs of classroom time and 6 hrs of homework.

If you are lagging behind, use the online course material [OCW] to catch up. There are also 1-2 buffer classes in each quarter, to help you. If you are already comfortable with the topics, the buffer classes gives you time to explore bonus topics.

**Lec 1 : Sample Space | Probability Axioms | Counting***Read*: [BT] Section 1.1, 1.2, 1.6. [OCW] Lectures 1, 4*Explore*: [WF] Chapter I Section 2-7, Chapter II Section 1-4

**Lec 2 : Conditional Probability | Bayes Rule***Read*: [BT] Section 1.3, 1.4. [OCW] Lecture 2.*Explore*: [WF] Chapter 5, Sections 1, 2, 3

Tutorial 1:

Test 1:

**Lec 3: Independence | Random Variables***Read*: [BT] Section 1.5, 2.1-2.4. [OCW] Lecture 3, 5.*Explore*: [WF] Chapter 5, Section 3, 4. Chapter 9 Sections 1-4.

**Lec 4: Problem Solving | PMF | Expectation***Read*: [BT] Sections 2.1–2.3, [OCW] Lecture 5, Recitations 3, 5*Explore*: [WF] Chapter 9, Sections 1-4

Tutorial 2:

Office Hrs 1

Test 2:

**Lec 5: Expectation | Variance | Conditioning of Random Variables***Read*: [BT] Sections 2.2–2.4, [OCW] Lecture 6*Explore*: [WF] Chapter IX*Solve*: [OCW] Recitations 6

**Lec 6: Multiple Random Variables | Examples: Balls and Bins, Sum of Bernoulli Trials | Independence of RVs***Read*: [BT] Sections 2.4 - 2.7, [OCW] Lecture 7.*Explore*: [WF] Chapter IX*Solve*: [OCW] Problem Set 4, Quiz 1 (Fall 2009) Problem B, Quiz 1 (Fall 2010) Problem 1

Tutorial 3

Office Hours 2

**Lec 7: Continuos RVs****Lec 8: Multiple Continuos RVs****Lec 9: Continuos Bayes****Lec 10: Markov | Chebyshev****Lec 11: Sum of RVs | Chernoff****Lec 12: Chernoff****Lec 13: Central Limit Theorem****Lec 14: Process | Bernoulli Process****Poisson Process - I****Markov Chains I****Markov Chains II****Markov Chains III****Markov Chains IV****Classical Stat. Inference**: (2 lecs) Point Estimates for Mean, Varience | Interval Estimates | Maximum Likelihood | Hypothesis Testing | Linear Regression**Information Theory (2 lecs by Prof. Lalitha)****Bayesian Stat. Inference****Multidimensional Gaussian’s & Kalman Filters**

[BT] Introduction to Probability, 2nd Edition by Dimitri P. Bertsekas and John N. Tsitsiklis./

[HPN] Introduction to Probability, Statistics and Random Processes. by Hossien Pishro-Nik. Texbook available online: https://www.probabilitycourse.com/

[WF] An Introduction to Probability Theory and Its Applications, Volume 1 by William Feller.

[SR] Introduction to Probability and Statistics for Engineers and Scientists by Sheldon M. Ross.

**Available in Library**.[OCW] Probabilistic Systems Analysis and Applied Probability Online Resource. MIT OCW https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/index.htm