Discrete Uniform Sum Random Variable Generator

The discrete uniform sum distribution is the sum of k discrete uniform random variables that are bounded between a and b. When k = 1, the distribution is uniform; when k = 2, the distribution is triangular. As k grows, the uniform sum model approaches a Gaussian probability model.

You can use the tool below to generate N random variables from a discrete uniform sum distribution. For example, if simulating the sum of 3 rolled dice, you set a = 1, b = 6, and k = 3.

a (min) =     b (max) =     k = N =
Decimal Precision: integers only	Display comma separated vertical

The mean, median, mode, variance, and skewness of the discrete uniform sum distribution are:

mean = k(a+b)/2
median = k(a+b)/2
mode = k(a+b)/2     if k is at least 2
variance = [k(b - a + 1)² - k]/12
skewness = 0

The tool above is useful in creating simulations of dice sums. For example, suppose you roll two 8-sided dice (octahedrons) where the faces are labeled with the numbers 1 through 8. If you want to simulate this operation 100 times, select a = 1, b = 8, k = 2, and N = 100. This will generate a set of numbers whose mean, median, and variance are close to 9, 9, and 10.5 respectively.

You can further analyze the simulation using the descriptive statistics calculator.

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