Homework 1
Foundational statistical concepts: populations, samples, descriptive vs. inferential statistics, and core terminology.
Statistics 25/26
All notes live here — interactive homework assignments and statistical analysis.
Course Overview
This collection presents interactive homework assignments for the Statistics course (2025/26 academic year). Each assignment combines theoretical foundations with hands-on computational analysis, demonstrating statistical concepts through visualizations, simulations, and real-world datasets.
Homework Assignments
Homework 2
Statistical distributions with SQL queries, Caesar cipher cryptanalysis using χ² distance, and automated multi-language detection.
Homework 3
RSA encryption demonstration, letter frequency analysis, and cryptographic character mappings with visual comparison charts.
Homework 4
Law of Large Numbers simulation: convergence of relative frequencies with interactive Bernoulli trial visualizations.
Homework 5
Central tendency and dispersion measures: mean, median, mode, variance, standard deviation, and percentiles.
Homework 6
Online algorithms for streaming statistics: incremental mean and variance computation with interactive demonstrations.
Homework 7
Server security random walk simulation: trajectory analysis with Bernoulli processes, probability of breach scenarios, and interactive security score visualizations.
Homework 8
Mathematical theory of random walks: binomial coefficients, Pascal's triangle, binomial expansion, Fibonacci connections, and combinatorial path enumeration.
Homework 9
Measure theory and probability spaces: Kolmogorov axioms, subadditivity derivation, and inclusion-exclusion principle with interactive Venn diagrams.
Homework 10
Poisson process simulation: continuous-time stochastic counting processes with trajectory analysis and applications to network traffic modeling.
Homework 11
Brownian motion and continuous random walks: continuous-time, continuous-space stochastic processes with Normal increments via the Box-Muller transform.
Course Thesis
Online Algorithms for Real-Time Statistical Computations
View Repository & PDFAn extensive investigation into streaming estimators, change-point detection methods, and online learning techniques applied to cybersecurity. The core methodology explores algorithms such as Welford's moving variance, CUSUM/EWMA control charts, and Stochastic Gradient Descent (SGD) for scalable intrusion anomaly detection on network traffic streams.