Uniform Probability Mass Function

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A Uniform Probability Mass Function is a discrete probability function that is a uniform probability function.



References

2017

  • (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Discrete_uniform_distribution Retrieved:2017-7-16.
    • In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

      A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

      The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by all integers in an interval [a,b], so that a and b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n). With these conventions, the cumulative distribution function (CDF) of the discrete uniform distribution can be expressed, for any k ∈ [a,b], as : [math] F(k;a,b)=\frac{\lfloor k \rfloor -a + 1}{b-a+1} [/math]

2011