The Statistics package includes 9 discrete probability distributions and commands for manipulating and creating discrete random variables.
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Consider a binomial random variable. Unlike continuous random variables, discrete random variables are defined by their probability function rather than their probability density function.
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| (2.2) |
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| (2.3) |
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| (2.6) |
The Statistics package also allows for both numeric and symbolic manipulation of random variables and distributions. Consider the negative binomial distribution with symbolic parameters.
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| (2.8) |
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| (2.12) |
Further, the Statistics package supports the probability table. This distribution is used to associate probabilities with the integers 1..n, for any n. Consider a case of n = 5.
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The Statistics package also supports the empirical distribution, which is effectively a probability distribution built around a data sample. The probability of each element is equal to its frequency in the data sample.
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| (2.17) |
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| (2.18) |