Simulating Stochastic Differential Equations
From Brownian Motion to General Processes using the Euler-Maruyama Method This project explores the numerical simulation of stochastic processes, specifically…
Simulating a Counting Process via Discretization
This report details the simulation of a counting process over a time interval T, where events, termed “successes,” occur independently and…
Interpretations Of Probability
In the landscape of mathematics and statistics, the concept of probability is foundational, yet its interpretation has been a subject…
A Deeper Analysis of the Server Security Random Walk
This report discusses the analogies between the server security simulation (HMWK 7) and a classic Bernoulli process simulation of the…
Random Walks in Server Security
A server receives security updates weekly for n weeks. There are m independent attackers each week; each attacker succeeds in…
Derivation of Recurrence Relationships
Arithmetic Mean The arithmetic mean, often denoted as μ or x̅, for a dataset of n observations x1,x2,…,xn is defined as: We want to…
Concepts of location and dispersion measures
In statistical analysis, a central objective is to transform complex and extensive datasets into concise and interpretable summaries. When dealing…
Law of Large Numbers
The Law of Large Numbers is a fundamental theorem in probability theory that describes how the average of results from…
RSA
Introduction to RSA Encryption RSA (Rivest-Shamir-Adleman), developed in 1977 by Ron Rivest, Adi Shamir, and Leonard Adleman, represents one of…
Dataset
A dataset is a systematically organized collection of data, typically structured in a way that facilitates analysis and interpretation. In…