Uniform Distribution (discrete)
In probability theory and statistics, the discrete uniform distribution is a probability distribution whereby a finite number of equally spaced 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 equally spaced outcomes equally likely to happen".
If a random variable has any of possible values that are equally spaced and equally probable, then it has a discrete uniform distribution. The probability of any outcome is . A simple example of the discrete uniform distribution is throwing a fair die. The possible values of 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 uniform distribution no longer fits since the values from 2 to 12 do not have equal probabilities.
The cumulative distribution function (CDF) of the discrete uniform distribution can be expressed in terms of a degenerate distribution as
where the Heaviside step function is the CDF of the degenerate distribution centered at, using the convention that
Read more about Uniform Distribution (discrete): Estimation of Maximum, Random Permutation
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