Projects

Statistics and cybersecurity are intrinsically linked, as statistical analysis and data science are essential for understanding threats, detecting anomalies, and developing effective security measures in large, complex computer networks. Key statistics from 2024-2025 highlight the escalating financial costs of cyberattacks, increased frequency of data breaches and ransomware incidents, the prevalence

A dataset is a collection of data points, and its distribution describes how those values are spread out and how frequently each value occurs. Data Distribution A distribution is the representation of the frequency of each value or interval within a dataset. A distribution can be used to better understand

Quadgram Solver — Annealed Hill-Climb + Double Swap Paste your ciphertext (space-separated tokens or continuous encrypted text), optionally load a full quadgram table, then press Run. Default settings work well; increase iterations/restarts for longer texts. Quadgram table (optional) — format: TION 0.00312 per line. You can load a full table for

What is the Law of Large Numbers (LLN)? The Law of Large Numbers (LLN) is a fundamental concept in probability and statistics. It states that as the number of independent trials of a random experiment increases, the sample average of the outcomes will get closer and closer to the expected

Measures of Location Measures of location are used to summarize the data with just one value. They try to capture with a single number what is typical of the data. What single number is most representative of an entire list of numbers? We will study three common measures of location:

Derivation of recurrence relations and efficient implementation for incremental statistical updates. Abstract This article derives and demonstrates the online computation of the arithmetic mean and variance through Welford’s algorithm. The method allows incremental updates as new data points arrive, offering improved numerical stability, constant memory usage, and computational efficiency

In this simulation, we study a server that receives weekly security updates for n weeks. Each week, m independent attackers attempt to breach the system, and each attacker has a probability p of succeeding. The probability that the server is breached during a given week is: q = 1 − (1 − p)

Analogies Between the Bernoulli Process Simulations and the Law of Large Numbers Both homework projects explore how randomness reveals order through repetition. In both cases, we simulate a Bernoulli process — a sequence of independent trials where each trial has only two possible outcomes, often labeled as success (1) or failure

Probability is a fundamental concept in statistics, mathematics, and many scientific disciplines. It quantifies the uncertainty associated with events chosen from a some universe of events. However, not everyone agrees on the meaning or interpretation of probability. There are several schools of thought, each providing its own perspective. Frequentist Interpretation

Simulation idea We want to simulate a counting process over a time interval T, where events happen: * Independently * Uniformly in time * With constant average rate λ We approximate this by dividing T into n small intervals. For each interval: $$\text{Probability of an event} = \frac{\lambda}{n}$$ This is equivalent