Notebook Collection

Author
Affiliation

Prof. Nipun Batra

Indian Institute of Technology, Gandhinagar

Keywords

probability, statistics, data visualization, jupyter notebooks, python, education, machine learning, data science, interactive learning

Learning Path

These 24 notebooks are organized by topic and difficulty. Use the sidebar navigation for structured learning or browse the complete collection below.

Foundations

Start with basic probability concepts and mathematical foundations.

Random Variables & Distributions

Learn about discrete and continuous distributions, PMFs, PDFs, and CDFs.

Statistical Concepts

Explore expectation, variance, independence, and key theorems.

Advanced Topics

Study multivariate distributions and joint probability concepts.

Machine Learning

Apply probability concepts to PCA, classification, and embeddings.

Data Science Tools

Master NumPy, Pandas, and Matplotlib for data analysis.

Getting Started

New to the subject? Start with the “Getting Started” section in the sidebar.

Looking for specific topics? Use the search and filter options below.

Want to run locally? See the README for setup instructions.

CDF for Discrete Random Variables

Understanding cumulative distribution functions for discrete random variables with categorical distributions and practical examples of logistic regression

Feb 11, 2025

Cumulative Distribution Functions and Inverse Sampling

A comprehensive exploration of cumulative distribution functions (CDFs), their properties, and applications in random number generation through inverse transform sampling. Covers both discrete and continuous distributions with practical implementations.

Mar 6, 2025

Data Analysis Quiz - Pandas GroupBy Operations

Practical exercises and quiz problems focusing on pandas groupby operations and data aggregation techniques

Feb 11, 2025

Distributions in 2D

Exploring bivariate probability distributions including 2D normal and uniform distributions, with practical examples using PyTorch and real-world height-weight data

Mar 17, 2025

Images and Joint Distributions

Exploring joint distributions through image data analysis using PCA dimensionality reduction and visualization of multi-dimensional probability distributions

Mar 18, 2025

Independent and Identically Distributed (i.i.d) Random Variables

Understanding the concept of independent and identically distributed random variables, their properties, and applications in probability theory and statistics

Mar 17, 2025

Interactive Data Exploration with Jupyter Widgets

Interactive data exploration and visualization using Jupyter widgets with pandas and matplotlib

Jan 22, 2025

Introduction to Matplotlib

Comprehensive introduction to matplotlib for data visualization

Jan 17, 2025

Introduction to NumPy

A comprehensive introduction to numerical computing with NumPy, covering array creation, manipulation, indexing, slicing, and fundamental operations for scientific computing

Jan 6, 2025

Introduction to Pandas

A comprehensive introduction to Pandas library for data manipulation and analysis, covering data structures, indexing, merging, grouping, and advanced operations

Jan 13, 2025

Introduction to Probability and Statistics

An introduction to probability theory, random number generation, and statistical concepts using Python

Jan 5, 2025

Introduction to Random Variables

A comprehensive introduction to random variables, their mathematical foundations, and practical applications. Covers discrete random variables, probability mass functions, and the relationship between histograms and theoretical distributions.

Dec 5, 2024

Joint Distribution Properties

Exploring properties of joint probability distributions, including independence, covariance, correlation, and bivariate normal distributions with practical examples

Mar 24, 2025

Law of Large Numbers and Central Limit Theorem

Interactive exploration of the Law of Large Numbers and Central Limit Theorem using Monte Carlo simulations with Bernoulli random variables

Apr 6, 2025

Mathematical Expectation and Law of Large Numbers

A comprehensive exploration of mathematical expectation, running averages, and the Law of Large Numbers with practical examples including dice rolls, coin flips, and financial simulations

Feb 17, 2025

PMF and their applications

Probability Mass Functions (PMF) are fundamental tools for describing the behavior of discrete random variables. A PMF tells us the probability that a discrete random…
Feb 11, 2025

Principal Component Analysis

Principal Component Analysis (PCA) is one of the most fundamental techniques in data science and machine learning. It serves as a cornerstone for dimensionality reduction…
Apr 14, 2025

Probability Density Functions and Continuous Distributions

A comprehensive exploration of continuous probability distributions including Normal, Laplace, Log-Normal, Gamma, Uniform, Beta, and Exponential distributions. Covers theoretical foundations, real-world applications, and practical implementation with PyTorch.

Feb 17, 2025

Probability Mass Functions and Common Discrete Distributions

A comprehensive exploration of discrete probability distributions including Bernoulli, Categorical, Binomial, Poisson, and Geometric distributions. Covers theoretical foundations, practical applications, and real-world modeling scenarios.

Feb 11, 2025

Probability Theory Fundamentals

Introduction to fundamental probability concepts including sample spaces, events, and probability laws with practical Python implementations

Feb 2, 2025

Random Vector

25000 rows × 2 columns
Apr 14, 2025

Set 

import matplotlib.pyplot as plt
import numpy as np
import torch 
import pandas as pd
# Retina mode
%matplotlib inline
%config InlineBackend.figure_format = 'retina'
Dec 7, 2024

Sum of Random Variables

Understanding the distribution of sums of random variables through simulation and theory, covering both discrete and continuous cases

Apr 1, 2025

Word Embeddings and Vector Angles

Understanding vector similarities and angles in word embeddings using cosine similarity and vector operations for natural language processing applications

Mar 23, 2025
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Citation

BibTeX citation:
@online{batra,
  author = {Batra, Nipun},
  title = {PSDV {Teaching} {Resources:} {Interactive} {Notebooks} for
    {Probability,} {Statistics,} and {Data} {Visualization}},
  url = {https://nipunbatra.github.io/psdv-teaching/},
  langid = {en}
}
For attribution, please cite this work as:
Batra, Nipun. n.d. “PSDV Teaching Resources: Interactive Notebooks for Probability, Statistics, and Data Visualization.” https://nipunbatra.github.io/psdv-teaching/.