Statistical Inference Course Homeworks and Project - University of Tehran (Fall 2023)

This repository contains homework assignments and the final project for the Statistical Inference course at the University of Tehran. The assignments and project involve the application of statistical methods such as probability theory, hypothesis testing, ANOVA, bootstrapping, and regression analysis to real-world data.

Homeworks Overview

Homework 1:

• Topics: Probability theory, random variables, birthday problem, Bayesian analysis, Monte Carlo methods.
• Key Problems:
  • Alarm system reliability.
  • Analyzing the birthday problem using probability and simulation.
  • Bayesian analysis of a taxi identification scenario.
  • Monte Carlo simulation to estimate π.

Homework 2:

• Topics: Confidence intervals, hypothesis testing, randomized surveys, sample size determination.
• Key Problems:
  • Application of the Central Limit Theorem (CLT) for dice probabilities.
  • Statistical estimation and variance calculation for sensitive surveys.
  • Simulating sampling distributions for health data.

Homework 3:

• Topics: Bootstrapping, ANOVA, p-value correction, regression analysis.
• Key Problems:
  • Constructing confidence intervals using bootstrapping on diabetes data.
  • Comparing battery lifetimes using ANOVA.
  • Regression analysis between height and weight in a dataset.

Final Project Overview

The final project involves working with a dataset to apply several statistical methods:

• Exploratory Data Analysis: Visualizing and summarizing categorical and numerical variables.
• Parametric Inference and Estimation: Estimating parameters and constructing confidence intervals.
• Hypothesis Testing: Formulating and testing hypotheses, including ANOVA.
• Regression Analysis: Exploring relationships between variables using regression techniques.