Ultimi Articoli
Simulating and Analyzing Brownian Motion: The Continuous Evolution of Stochastic Processes
Introduction: The Evolution of Stochastic Processes In our previous studies, we explored: Now we complete the picture with Brownian Motion (also called the Wiener Process): continuous states, continuous time. The connection between these processes is deep: Brownian motion emerges as…
Simulating and Analyzing a Counting Process: The Poisson Approximation and the Meaning of λ
Counting processes represent systems where discrete events (“arrivals”) happen at random points in time. This…
Foundations of Probability: Interpretations, Axioms, and Measure Theory
Though probability theory is an indispensable tool in science and engineering, a centuries-old debate persists…
On the Binomial Unity of Stochastic Processes: Structural Equivalence Between Law of Large Numbers Demonstrations and Security Server Models
This work explores the deep mathematical connections between two seemingly different stochastic processes: the classical…
Binomial Random Walks in Server Security
We analyze the security of a server system over a period of n weeks. Each week, the…
Online Mean and Variance: Theoretical Derivation and Algorithm Implementation
In modern analytics, static datasets are increasingly rare. Data is now generated as continuous streams from domains such as financial trading, IoT sensors, and digital media platforms. Conventional batch-processing statistical techniques, which require reprocessing the complete historical dataset for every…
Measures of Central Tendency and Dispersion
Measures of location and central tendency In statistics, summarizing a complex dataset with a single,…
The Law of Large Numbers: Theory and Simulation
Introduction to the Law of Large Numbers: The Law of Large Numbers (LLN) is one…
RSA: Theory and Practical Application
Principles and Key Generation RSA is an asymmetric encryption system (public key/private key). This means…
From Datasets to Decryption: A Statistical Approach to Cryptanalysis (second homework)
From Raw Data to Distributions The foundation of any statistical analysis is the dataset, a structured…