Galton Board
The Galton Board (also known as a quincunx or bean machine) is a physical device invented by Sir Francis Galton to demonstrate the Central Limit Theorem and the emergence of the Normal Distribution from random processes. It consists of a vertical board with interleaved rows of pins. Balls dropped from the top bounce left or right at each pin, accumulating in bins at the bottom.
Mechanism
- Random Walk: Each ball undergoes a series of independent Bernoulli trials (left/right deflection) as it descends.
- Binomial Distribution: The position of a ball in the final bins follows a Binomial Distribution based on the number of rows and the probability of deflection.
- Convergence: As the number of rows (trials) increases, the distribution of balls in the bins approximates a Gaussian Distribution (bell curve), illustrating how aggregate randomness yields predictable order.
Related Concepts
- Law of Large Numbers
- Entropy
- Stochastic Processes