# Probability & Statistics

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).

## How to ace the course with minimum effort?

1. Attend all the lectures (90 mins each).
2. Read the corresponding topics in the textbook on the same day (1 hr after each lecture).
3. Solve the problems for the previous lecture before the next lecture (2 hr after each lecture).
4. Ask doubts and clear them during tutorials (60 mins).
5. 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.

## Lectures

• 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

• Mid Sem Exam

• Lec 14: Process | Bernoulli Process

• Poisson Process - I

• Markov Chains I

• Markov Chains II

• Markov Chains III

• Markov Chains IV

• Test 5

• Quiz 2

• 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

• Final exam