ES 114 IIT Gandhinagar

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Lectures

Each lecture lists its reading first (slides, handwritten slides and cheat sheet), then its videos, then practice: notebooks and apps. Slides marked (Chan) are from Stanley Chan's Introduction to Probability for Data Science. Notebooks and their source are in psdv-teaching, which also lists all rendered notebooks.

NotesSlidesCheat sheetFull recordingNotebookInteractive labCodeReading

Python for data1–5Sets and probability6–11Random variables12–18Multiple random variables19–24Limit theorems, random vectors and PCA25–27

YouTube playlist of recordingsAll 15 cheat sheets

Python for data

Lectures 1–5

Lecture 01	Introduction and logistics
Lecture 02	NumPy	Cheat sheet: NumPy and pandas Video: Introduction to NumPy Notebook
·	Lab 1: NumPy	Colab notebook
Lecture 03	Pandas	Cheat sheet: NumPy and pandas Video: Introduction to pandas Notebook
Lecture 04	Matplotlib	Cheat sheet: Plotting and honest charts Video: Introduction to Matplotlib Notebook
·	Lab 2: Pandas Held over two lab sessions.	Colab notebook
Lecture 05	Jupyter widgets	Video: Jupyter widgets tutorial Notebook

Sets and probability

Lectures 6–11

Lecture 06	Set theory	Slides (Chan)Cheat sheet: Sets, sample spaces and events Notebook
Lecture 07	More set theory questions	Colab notebook
Lecture 08	Set theory (continued)	Slides (Chan)Handwritten slides
Lecture 09	Probability	Slides, part 1 (Chan)Slides, part 2 (Chan)Handwritten slides
Lecture 10	Conditional probability and independence	Slides: Conditional probability (Chan)Slides: Independence (Chan)Handwritten slidesCheat sheet: Conditional probability, independence and Bayes' rule
Lecture 11	Bayes' theorem and total probability	Slides (Chan)Handwritten slides (continued)Cheat sheet: Conditional probability, independence and Bayes' rule

Random variables

Lectures 12–18

Lecture 12	Random variables With a discussion of Quiz 1.	Slides (Chan)Cheat sheet: Random variables and PMFs
Lecture 13	Probability mass function	Slides (Chan)Cheat sheet: Random variables and PMFs Video: PyTorch distributions (discrete) Notebook
Lecture 14	Discrete random variables and expectation	Slides (Chan)Handwritten slides: expectation and moments of PMFsCheat sheet: Discrete distributions Video: The binomial and Poisson distributions (Luis Serrano) Notebook
Lecture 15	Moments	Slides (Chan)Handwritten slides (continued)Handwritten slides: continuous random variablesCheat sheet: Expectation and variance
Lecture 16	Continuous random variables and the coin-flip game	Cheat sheet: Continuous distributions and densities Notebook: ExpectationNotebook: PDF of a continuous random variable
Lecture 17	Expectation and moments of continuous random variables	Handwritten slides: expectation and moments of PDFsCheat sheet: Expectation and variance Notebook: Expectation (continued)Notebook: PDF of a continuous random variable (continued)
Lecture 18	Cumulative distribution function	Handwritten slides: CDFCheat sheet: CDFs and sampling Notebook: CDF

Multiple random variables

Lectures 19–24

Lecture 19	Joint PDF and CDF, 2D distributions and GeoGebra	Slides: Joint PDF and CDF (Chan)Cheat sheet: Joint distributions Video: How to set up double integralsVideo: Instructor's demo on GeoGebra Notebook: 2D distributionsHugging Face Space: 2D distributions
Lecture 20	Joint expectation	Slides: Joint expectation (Chan)Handwritten slides: joint expectation Notebook: Embeddings
Lecture 21	Correlation and covariance	Slides: Covariance (Chan)Handwritten slides: joint expectationCheat sheet: Covariance, correlation and the bivariate normal Notebook: Joint distributions
Lecture 22	Conditional distributions	SlidesCheat sheet: Joint distributions
Lecture 23	Sum of random variables	Handwritten slides: sum of random variablesSlides: Sum of random variables (Chan)Slides: X + Y (Chan)Cheat sheet: Sums of random variables, LLN and CLT Video: Convolutions, why X+Y in probability is a beautiful mess (3Blue1Brown) Notebook: Sum of random variables
Lecture 24	Transformation of random variables	Slides: Transformation Notebook: Transformation

Limit theorems, random vectors and PCA

Lectures 25–27

Lecture 25	Law of large numbers and inequalities	Handwritten slides: LLNSlides: Jensen's inequality (Chan)Slides: Markov and Chebyshev inequalities (Chan)Cheat sheet: Sums of random variables, LLN and CLT Notebook: LLNStreamlit app: LLN and CLT
Lecture 26	Random vectors and the multivariate normal distribution	Slides: Derivation of the bivariate normal distributionSlides: Random vectors (Chan)Slides: Multi-dimensional Gaussian (Chan)Slides: Gaussian whitening (Chan)Cheat sheet: Covariance, correlation and the bivariate normalCheat sheet: Random vectors and PCA Notebook: Random vectorsStreamlit app: Normal shape
Lecture 27	Principal component analysis	Slides: PCACheat sheet: Random vectors and PCA Video: Eigenvectors and eigenvalues (3Blue1Brown)

Cheat sheets are two-page A4 summaries; the ones on counting and the complement rule and on likelihood and log probabilities are listed with the others on the teaching page. Lab vivas and quizzes are on the Assessment page.