ES 114: Probability, Statistics and Data Visualization
IIT Gandhinagar
Sem II - 2025-26
Instructor: Mayank Singh (email: singh.mayank@iitgn.ac.in)
Class Schedule:
English Section: C1 (Monday 10:00 - 11:20, Jasubhai Auditorium)
Hindi Section: D1 (Tuesday 10:00 - 11:20, 11/102)
Lab Schedule:
Students with Laptop: K2 (Thursday 14:00 - 15:20, Jasubhai Auditorium)
Students without Laptop: K2 (Thursday 14:00 - 15:20, 10/104)
Communication Google group: es114-2025.pvtgroup@iitgn.ac.in
Teaching Assistants (GTF, PGTA, UGTA):
Rishabh Mondal | rishabh.mondal@iitgn.ac.in
Ayush Shrivastava | shrivastavaayush@iitgn.ac.in
Jenil Pradipkumar Patel | jenil.patel@iitgn.ac.in
Koppolu Charan Teja | 24210056@iitgn.ac.in
Shivansh Gupta | shivansh.gupta@iitgn.ac.in
Abhishek Mahor | abhishek.mahor@iitgn.ac.in
Advait Pardeshi | advait.pardeshi@iitgn.ac.in
Akhil Maan | akhil.maan@iitgn.ac.in
Ayush Mahendrakumar Thakar | ayush.thakar@iitgn.ac.in
Isha Snehalbhai Dave | isha.dave@iitgn.ac.in
Kolla Jaya Prakash | kolla.jaya@iitgn.ac.in
Naren Kumar S | naren.kumar@iitgn.ac.in
Hari Prapan | 23120043@iitgn.ac.in
Miral Aravindbhai Vaghasiya | miral.vaghasiya@iitgn.ac.in
Nakul Shravankumar Mistry | 24210066@iitgn.ac.in
Pankaj Kumar | 24210071@iitgn.ac.in
Ankit Dhurve | ankit.dhurve@iitgn.ac.in
Arjun K Reju | arjun.reju@iitgn.ac.in
Krudant Krushna Randai | krudant.randai@iitgn.ac.in
Manan Ashokkumar Solanki | manan.solanki@iitgn.ac.in
Isha Jain | isha.jain@iitgn.ac.in
Prerequisite (Optional)
First Year Undergrad Courses
Course Contents
1. Computational Tools
Statistical Data Analysis using Python/R
Introduction to Relevant Libraries
2. Basic Probability
Set Theory and Probability Spaces
Axioms of Probability
Probability Assignment for Discrete and Continuous Spaces
Combinatorics
Conditional Probability, Independence, and Mutual Exclusiveness
Law of Total Probability
Bayes’ Rule
Illustrative Examples
3. Random Variables
Discrete and Continuous Random Variables
Probability Mass Function (PMF) and Probability Density Function (PDF)
Transformation (Function) of Random Variables
Cumulative Distribution Function (CDF)
Moments and Characteristic Function
Examples of Common Random Variables and Applications
4. Two Random Variables and Random Vectors
Joint PMF and PDF
Conditional PMF and PDF
Joint and Conditional Moments
Joint Characteristic Function
Covariance, Correlation Coefficient, and Covariance Matrix
Dependence and Correlation
Transformation, Examples, and Applications
5. Statistical Inference
Confidence Intervals
Hypothesis Testing: Critical Value Test, p-Value Test, Z-Test, and t-Test
Neyman–Pearson Test
Receiver Operating Characteristic (ROC) and Precision–Recall (P–R) Curves
Applications
6. From Data to Visualization
Data Handling:
Numbers, Strings, Sequences, Tables, and Functions on Tables
Visualization Techniques:
Categorical and Numerical Distributions
Overlaid Graphs
Statistical Visualization: Line Charts, Bar Charts, Contour Plots
Spatial Data Visualization and Network Visualizations using Python Libraries
Visualizing Probability Distributions
Interactive Visualization and Advanced Topics:
Curve Fitting, Regression, Clustering
Linear and Non-linear Classification
Dimensionality Reduction (e.g., n-D to 2-D): Principal Component Analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE)
Examples and Applications across Various Engineering Disciplines
Lecture Slides (Slides and Colab Notebooks)
Introduction to Numpy [Colab Notebook, Official Documentation]
Introduction to Pandas [Colab Notebook, Official Documentation]
Lab Material
Setting Up Your Python Development Environment [BlogPost]
Numpy Lab : Introduction to Numpy [BlogPost]
Numpy Practice Problem [Colab Notebook]
Grading Policy & Schedule
6 Assignments (30%)
Two quizzes (30%)
Mid and End-semester Exam (40%)
There will be no makeup examinations for students who are absent.
Books
Chan, Stanley. “Introduction to Probability for Data Science.” The University of Michigan Library, Michigan Publishing (2021). Free Digital Copy
Adhikari, Ani, John DeNero, and D. Wagner. “Computational and Inferential Thinking: The Foundations of Data Science.” Second Edition. The University of California, Berkeley (2019). Free Digital Copy
Deisenroth, Marc Peter, A. Aldo Faisal, and Cheng Soon Ong. Mathematics for Machine Learning. Cambridge University Press, 2020. Free Digital Copy
Spiegelhalter, David. The Art of Statistics: Learning from Data. Penguin UK, 2019.
Rougier, Nicolas. Scientific Visualization: Python+ Matplotlib. 2021. Free Digital Copy