Wednesday, October 24, 2012

Modified Galton Board: The Go - No Go Problem

  The Galton board is used to illustrate how one can arrive at a normal distribution using a natural process. To see how this works we can use a modified model of the Galton board which is more general in nature.
 Consider the simple two event mechanism to the left. In each interval of time the device can either advance one step to the right or not advance. If p is the probability of advance then q=1-p is the probability of no advance since these are the only two possible events.

 The number of paths to a point in the tree to the left is a Bernouli coefficient. The probability of reaching a point on a line after n intervals is a binomial distribution.

Binomial Distribution
 For p=3/4 the average distribution of 1024 objects after n intervals of time is shown to the left. One would expect the results of an actual experiment to deviate slightly.

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