discrete uniform distribution
lower bound parameter
upper bound parameter
The discrete uniform distribution is a discrete probability distribution with probability function given by:
subject to the following conditions:
Note that the DiscreteUniform command is inert and should be used in combination with the RandomVariable command.
X ≔ RandomVariable⁡DiscreteUniform⁡a,b:
The variance of X is a somewhat messy expression, because of all the ceil and floor functions.
If we know that a and b are integers, we can apply these assumptions to make the expression easier to read.
Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.
Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.
Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
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