Galton Board App 與 Art of Stat: Concepts 使用情況與統計

Unlock the power of probabilities and explore the beauty of mathematics in motion with the Galton Board App. This innovative application transforms your mobile device into a dynamic, interactive probability demonstrator that brings centuries-old mathematical concepts to life. The app utilizes your iPhone's and iPad's gyroscope capabilities, creating an immersive experience where the beads appear as if they are rolling around inside your device. The Galton Board was invented by Sir Francis Galton in 1873 to illustrate the binomial distribution. Through our app, we've recreated this educational tool to demonstrate how, with a large number of beads and rows of hexagons, it approximates the normal distribution - a concept known as the Central Limit Theorem. Key Features: • An interactive Galton Board that displays the principles of probabilities and the binomial distribution. • Detailed explanations of related mathematical concepts, including probability theories, independent identically distributed (IID) random variables, regression to the mean, the law of large numbers, the random walk, the Gambler's Fallacy, and more. • A "Stock Market Data" version, simulating the probabilities of a range of historical monthly market returns, and demonstrating their correlation with the binomial distribution. • The 'Historical Monthly Return Beads' featured with the Stock Market Data, where beads fall through the board based on monthly historical returns for a choice of 20 index portfolios. • Pause or slow-motion options to study the bead movement and distribution patterns in detail. The Galton Board App is ideal for statistics, math, and stock market enthusiasts. It is not just an app, it's an immersive, hands-on approach to understanding probabilities, the binomial distribution, and the stock market behavior. Presented by Index Fund Advisors, this app is your go-to educational tool. Download now and embark on a fascinating journey into the world of probabilities and the "law of unreason" as referred to by Sir Francis Galton himself!