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Galton Box, or Probability Bean Machine (from Science Museum in Boston, taken in 2009) Brief Introduction: The device is invented by Sir Francis Galton in order to demonstrate how the normal or Gaussian distribution appears in nature or to demonstrate the central limit theorem. It comprises of a vertical board as seen the photo below with interleaved rows of pins. From the small hole on top of the board, a series of small pins are dropped, and then they bounce left or right in a random fashion whenever they hit the pins. In a sequal, all the pins (almost a thousand?) are collected into bins at the bottom and make one pattern. This will be resembled the Gaussian distribution. The Gaussian distribution is one of many things named after Johann Carl Friedrich Gauss (1777~1855), a German Scientist (Geodesy, Astronomy, Physics, Mathematics, etc.), who used it to analyze astronomical data, and determined the formula for its probability density function. See the movie clip below to understand the distribution. |
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In surveying, you cannot take a large number of repetitive measurements. But if you use survey techniques that normally give results that, when plotted, take the form of a probability curve, it is safe to assume that the errors associated with the survey measurements can be treated using random error distribution techniques.
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