Maths for CS I: Probability and Statistics

July, 2021

Prerequisites

Assumes basic knowledge of Discrete Maths and Algorithms. Highly recomended to brush up these concepts, especially if you had a break from academics. Some references are given bellow:

Schedule

Meetings

From 15th August - 30th September, 2021.

  • Live Lectures: Tuesdays and Fridays (12:00 pm - 1:30 pm)
  • Tutorials: Wednesday (9-1030AM)
  • Office Hours: Saturday (2:30 pm -4:00 pm). I will be available on Teams during the timings given bellow, for clearing any doubts. You can sent a direct message to me for joining.

Expected Workload

Students are expected to spent atleast 12 hrs per week. Roughly

  • 3+1 hrs attending lectures and tutorials
  • 4 hrs reading textbooks, references etc
  • 4 hrs solving assignments, quizes etc

Evaluations

  • 4 Light Quizzes (Wieghtage: 30%, Best 3 of 4). 20 min MCQ Test to check your understanding of definitions and to ensure that you have gone through reading material.
    • 28 August and 4, 18, 25 September.
  • 4 Assignments (Wieghtage: 30%, ^Best 3 of 4). Problems will require longer to solve. You will need to upload written solutions.
    Dates for Release | Submission | Marks Release given bellow:
    1. 12 Aug | 21 Aug | 28 Aug
    2. 21 Aug | 31 Aug | 5 Sept
    3. 31 Aug | 11 Sept | 18 Sept
    4. 11 Sept | 22 Sept | 29 Sept
  • 2 Deep Quizzes (Wieghtage: 40%). We will be doing timed exams of 1hr in moodle.
    1. Between 6-8 Sept | Mark release by 18th Sept.
    2. 30th Sept | Marks release by 10th Oct.

Lectures

1. Probability Basics

1.1 Probability and Counting | Infinite Sample Spaces

1.2 Axioms of Probability | Conditional Probability

  • Reading:
    • Section 1.4, Section 2 in HPN.
    • Secion 1.3, 1.6 in BT.
  • Explore:
  • Solve:

    • Let $X$ be number of nonempty bins and $Y$ be number of balls in the first bin. Find the probability of

      1. $X=i, Y=j$
      2. $X=i$ conditioned on $Y=j$

      for every $i,j$.

1.3 Conditional Probability | Independence

  • Reading:
    • Section 1.4, Section 2 in HPN.
    • Secion 1.3, 1.4 in BT.

1.4 Total Probability | Bayes' Rule

2. Random Variables

2.1 Random Variables | Expectation | Binomial Distrbution | Geometric Dist | Conditioning | Multiple RVs

  • Reading:
    • Section 3 in HPN.
    • Section 2 in BT.

2.2 Linearity of Expectation | Functions of Random Variables

  • Reading:
    • Section 3.2.2-3.2.3 in HPN.
    • Section 2.3-2.4 in BT.

2.3 Variance | Markov’s | Chebyshev’s Inequality

  • Reading:
    • Chapter 6 in AT.

2.4 Problem Solving | Poll Survey

  • Reading:
    • Chapter 6 in AT.

3. Advanced Random Variables

3.1 Poisson, Exponential, Continous Distributions

  • Reading:
    • Section 3.6, 4.1, 4.2 in AT.
    • Section 4.1, 4.2 in HPN.
    • Section 3.1, 3.2, 5.2 in BT.

3.2 Gaussian Distribution, Central Limit Theorem

  • Reading:
    • Section 4.3, 5.7 in AT.
    • Section 4.2.3, 7 in HPN.
    • Section 3.3 (Normal Dist), 4.2 (Convolutions), 7.1-7.4 (CLT) in BT.

4. Advanced Topics and Applications

4.1 Markov Chains

  • Reading:
    • Section 11.2 in HPN.
    • Chapter 6 in BT.

4.2 Markov Chains Convergence

  • Reading:
    • Section 11.2 in HPN.
    • Chapter 6 in BT.

References

Textbooks

Online Resources