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In the next two segments we provide an overview and then we discuss how a flip of a coin can be used to initiate the discussion of the statistical distribution.
The multinomial distribution
We can think of the multinomial distribution as the generalization of the binomial distirbution to large groups. This is precisely the kind of statistics needed to properly calculate probability of indistinguishale particles. The multinomial distribution provides the numer of ways that N particles can occupy M different states. This is precisely the kind of statistics needed to account for entropy since the entropy is proportional the number of ways we can distribute the energy at a given fixed total energy.
Continuous distributions
The previous ideas have already been shown to have a Guassian form in the limit of large numbers of occupied states. This limit is where we can apply the concept of a continuous distribution. Mathematically the most important function that can accurately represent a continuous distribution is the Gaussian.
Confidence limits
The next appplication consistst of defining the occupied area under the Gaussian measured out to a certain width (measured by the distance from the mean, which is also the center of the distirbution
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