The cover image was generated by Google Gemini.

While taking the graduate course Simulation Study, the instructor mentioned that the random numbers used in modern computers and programming are mostly not truly random in the strict sense, but rather pseudo-random numbers. Pseudo-random numbers are generated through mathematical algorithms that compute the next value based on the previous state. Therefore, as long as the algorithm, initial value (Seed), and current state are known, the entire random number sequence can theoretically be reproduced. This raises an interesting question: if every pseudo-random number can be calculated from the previous value, where does the very first number come from?

The cover image was generated by ChatGPT.

While attending The 35th South Taiwan Statistics Conference, I first learned about control charts from an experienced professor who had spent many years working in manufacturing environments. Intrigued by the concept, I decided to spend some time organizing my notes and gaining a foundational understanding of what control charts are.

Time complexity is used to describe how the computation time of an algorithm grows as the input size increases during its execution. Because the processing capabilities, hardware architecture, and system environment differ across computer devices, comparing algorithms solely based on actual execution time often fails to yield representative and portable conclusions. Therefore, time complexity is usually measured by the “number of basic operations executed,” and asymptotic complexity is employed to analyze the efficiency of algorithms, establishing a hardware-independent and universally applicable performance evaluation method.

This is a classic proof in mathematical statistics. That is, whether the variance of the sum of two random variables equals the sum of their variances.

The cover image was generated by ChatGPT.

Introduction

Logistic regression is a type of binary classification model derived from linear regression. Unlike linear regression, which fits a regression line that passes through the data points by minimizing the sum of squared distances, known as the least squares method. The goal of logistic regression is to find a decision boundary that clearly separates the data into two distinct classes.

Cover image generated by ChatGPT.

Introduction

How to calculate distance is an important aspect of modern statistical analysis. Choosing different distance metrics may lead to different results in statistical analysis methods. The following introduces commonly used distance metrics.

The cover image about Anscombe’s Quartet was generated by ChatGPT, and it used the following prompt: “The digital design highlights the title ‘Anscombe’s Quartet’ in bold, white sans-serif letters, centered against a dynamic abstract backdrop. The image is split into four colorful quadrants, each showcasing unique textures and patterns—ranging from painterly hues and curved lines to scattered circles and dots.”

Introduction

While listening to a presentation today, I happened to hear a term——Anscombe’s Quartet, a term I had never encountered before, yet it has significant implications in both statistics and data visualization.