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Published on Jul 13, 2007
The Central Limit Theorem says that the sum of enough identically distributed independent random variables looks like a normal distribution. Testing that via simulation. Particles follow a (simulated) brownian motion from the top center of the screen and have their point of impact recorded at the bottom. Each particle's path consists of 18000 events, whereby, at each, it moves vertically "-dy" and horizontally either "dx" or "-dx", with equal probability. As the particle reaches the bottom of the screen, a special impact event is recorded. The distribution of these impact events is, by construction, the distribution of the sum of the random variables giving the horizontal position changes at each time step. Note how the impact distribution is similar to the predicted gaussian.