IC252 - Probability and Statistics

IIT Mandi | Even Semester 2025 (January - July)

This repository contains my personal solutions to all assignments for the IC252 Probability and Statistics course at IIT Mandi.

By :: Taneshq Gupta (CSE-UG/IIT-MANDI).

Note: Assignment question papers are also included as PDF files in their respective assignment folders.

Course Overview

- Course Code: IC252

- Course Title: Probability and Statistics

- Institution: Indian Institute of Technology Mandi

- Semester: Even Semester 2025

- Duration: January - July 2025

Repository Structure

Assignment Solutions

- Assignment 1 - Basic probability simulations | Question Paper

- Dice rolling probabilities

- Ball drawing scenarios

- Monte Carlo simulations

- Assignment 2 - Birthday paradox and combinatorics | Question Paper

- Mathematical analysis vs Monte Carlo simulation

- Group arrangements and probability calculations

- Assignment 3 - Conditional probability | Question Paper

- Card selection problems

- Bayesian probability applications

- Assignment 4 - Hypergeometric distribution | Question Paper

- Urn simulation models

- Theoretical vs estimated probability distributions

- Assignment 5 - Gift distribution problems | Question Paper

- Derangement calculations

- Employee gift matching scenarios

- Assignment 6 - Discrete distributions | Question Paper

- Binomial distribution (inverse transform method)

- Poisson distribution (Knuth algorithm)

- Distribution plotting and analysis

- Assignment 7 - Custom probability distributions | Question Paper

- PDF and CDF implementations

- Inverse transform sampling

- Distribution visualization

- Assignment 8 - Bivariate distributions | Question Paper

- Exponential distribution sampling

- Correlation analysis

- Independence testing

- Joint and marginal distributions

- Assignment 9 - Couple seating problems | Question Paper

- Circular arrangement simulations

- Expected value and variance calculations

- Theoretical vs simulated results

- Assignment 10 - PDF analysis and comparison | Question Paper

- Multiple PDF implementations

- Statistical moment calculations

- Data fitting and visualization

Case Study

- Case Study - Real-world data analysis | Question Paper

- Week 1: Descriptive statistics and frequency analysis

- Week 2: Distribution fitting and parameter estimation

- Maximum likelihood estimation

- Confidence interval calculations

- Model comparison and visualization

Technologies Used

- Python 3.x

- Libraries:

- numpy - Numerical computations

- pandas - Data manipulation and analysis

- matplotlib - Data visualization

- scipy - Scientific computing and optimization

- random - Random number generation

- math - Mathematical functions

Key Concepts Covered

Key Algorithms

- Inverse Transform Method: For generating random samples from custom distributions

- Knuth Algorithm: Efficient Poisson random number generation

- Monte Carlo Integration: Numerical integration for complex probability calculations

- Maximum Likelihood Estimation: Parameter fitting for various distributions

Probability Theory

- Basic probability rules and axioms

- Conditional probability and Bayes' theorem

- Random variables and distributions

- Joint and marginal distributions

- Independence and correlation

Statistical Distributions

- Discrete distributions (Binomial, Poisson, Hypergeometric)

- Continuous distributions (Exponential, Uniform, Custom PDFs)

- Distribution parameter estimation

- Goodness-of-fit testing

Simulation Techniques

- Monte Carlo methods

- Inverse transform sampling

- Random number generation algorithms

- Bootstrap methods

Statistical Analysis

- Descriptive statistics

- Maximum likelihood estimation

- Confidence intervals

- Hypothesis testing

- Data visualization techniques

Running the Code

Prerequisites

pip install numpy pandas matplotlib scipy

Execution

Each assignment folder contains standalone Python scripts that can be executed directly:

cd ic252_assignment[X]
python3 [script_name].py

For assignments with data dependencies:

# Ensure CSV files are in the same directory
python a.py

Results and Insights

The assignments demonstrate practical applications of probability theory, including:

- Validation of theoretical results through simulation

- Real-world data analysis and modeling

- Comparison of different statistical approaches

- Visualization of complex probability concepts

Academic Integrity

These solutions represent my personal work for educational purposes. Please use them responsibly and in accordance with your institution's academic integrity policies.

Contact

For questions or discussions about the implementations, feel free to reach out.

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Probability is not about the odds. It's about belief in the existence of an alternative outcome, event, or reality. - Debasish Mridha