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# DiscreteUniformDistribution

 DiscreteUniformDistributionrepresents a discrete uniform distribution over the integers from to . DiscreteUniformDistributionrepresents a multivariate discrete uniform distribution over integers within the box .
• The probability for value in a discrete uniform distribution is constant for integers such that , and is zero otherwise. »
Probability density function of a univariate discrete uniform distribution:
Cumulative distribution function of a univariate discrete uniform distribution:
Mean and variance of a univariate discrete uniform distribution:
Median of a univariate discrete uniform distribution:
Probability density function of a bivariate discrete uniform distribution:
Cumulative distribution function of a bivariate discrete uniform distribution:
Mean and variance of a bivariate case:
Covariance:
Probability density function of a univariate discrete uniform distribution:
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Cumulative distribution function of a univariate discrete uniform distribution:
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Mean and variance of a univariate discrete uniform distribution:
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Median of a univariate discrete uniform distribution:
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Probability density function of a bivariate discrete uniform distribution:
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Cumulative distribution function of a bivariate discrete uniform distribution:
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Mean and variance of a bivariate case:
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Covariance:
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 Scope   (11)
Generate a set of pseudorandom numbers that have the discrete uniform distribution:
Compare its histogram to the PDF:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Compare the density histogram of the sample with the PDF of the estimated distribution:
Distribution parameters estimation for a multivariate discrete uniform distribution:
Estimate the distribution parameters from sample data:
Skewness:
Kurtosis:
With an infinitely large interval the kurtosis equals the kurtosis of UniformDistribution:
Multivariate discrete uniform distribution:
The components of discrete uniform distribution are uncorrelated:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Closed form for symbolic order:
Closed form for symbolic order:
Different mixed moments for a multivariate discrete uniform distribution:
Closed form for symbolic order:
Mixed central moments:
Closed form for symbolic order:
Mixed factorial moments:
Closed form for symbolic order:
Mixed cumulants:
Closed form for symbolic order:
Hazard function of univariate discrete uniform distribution:
In two dimensions:
Quantile function:
The marginals of a multivariate discrete uniform distribution are discrete uniform distributions:
A univariate marginal:
A bivariate marginal:
 Applications   (6)
The CDF of DiscreteUniformDistribution is an example of a right-continuous function:
A computer has 4 disks, numbered 0, 1, 2, 3, one of which is chosen at random on boot to store temporary files. Find the distribution of the chosen disk:
Find the probability that disk 1 is chosen:
Find the probability that an odd-numbered disk is chosen:
Simulate which disk is chosen on the next 30 boots:
A fair six-sided die can be modeled using a DiscreteUniformDistribution:
Generate 10 throws of a die:
Compute the probability that the sum of three dice values is less than 6:
Verify by generating random dice throws, in this case times three dice throws:
Verify by explicitly enumerating all possible dice outcomes:
Two fair dice are tossed. Find the distribution of the difference of the dice values:
Find the probability that the difference is at most 3:
Find the average difference:
Simulate differences for the 30 tosses:
In the game of craps [], two dice are thrown:
The resulting PDF can be tabulated as:
Find the probability of getting "snake eyes" []:
Or "boxcars" []:
Or "eighter from Decatur" []:
Or "little Joe" []:
The full list of probabilities:
Find the probability of losing in one throw or getting craps, i.e. any of the sums 2, 3, or 12:
Find the probability of winning in one throw, i.e., getting the sums 7 or 11:
A hypothetical R&D company has a holiday whenever at least one employee has a birthday. Find the number of employees that maximizes the days worked, assuming independent distributions of birthdays:
Find optimal number of employees:
Expected number of work days:
The probability of getting any real number except an integer between min and max is zero:
Truncation:
DiscreteUniformDistribution is not defined when min or max is not an integer:
Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:
Sum of fair dice: