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The bean machine, also known as the quincunx or Galton box, is a device invented by Sir Francis Galton to demonstrate the central limit theorem, in particular that the normal distribution is approximate to the binomial distribution. Among its applications, it afforded insight into regression to the mean or "regression to mediocrity". The machine consists of a vertical board with interleaved rows of pins. Balls are dropped from the top, and bounce left and right as they hit the pins. Eventually, they are collected into one-ball-wide bins at the bottom. The height of ball columns in the bins approximates a bell curve. Overlaying Pascal's triangle onto the pins shows the number of different paths that can be taken to get to each bin. A large-scale working model of this device can be seen at the Museum of Science, Boston in the ''Mathematica'' exhibit (currently closed). ==Distribution of the balls== If a ball bounces to the right ''k'' times on its way down (and to the left on the remaining pins) it ends up in the ''k''th bin counting from the left. Denoting the number of rows of pins in a bean machine by ''n'', the number of paths to the ''k''th bin on the bottom is given by the binomial coefficient . If the probability of bouncing right on a pin is ''p'' (which equals ''0.5'' on an unbiased machine) the probability that the ball ends up in the ''k''th bin equals . This is the probability mass function of a binomial distribution. According to the central limit theorem (more specifically, the de Moivre–Laplace theorem), the binomial distribution approximates the normal distribution provided that ''n'', the number of rows of pins in the machine, is large. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bean machine」の詳細全文を読む スポンサード リンク
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