Distribution of Sum of Discrete Uniform Random Variables

statistics uniform-distribution statistical-inference

Solution 1:

The distribution is asymptotically normal. Otherwise, the exact distribution is that of a normalized extended binomial coefficient, see "Polynomial Coefficients and Distribution of the Sum of Discrete Uniform Variables" by Camila C. S. Caiado and Pushpa N. Rathie at http://community.dur.ac.uk/c.c.d.s.caiado/multinomial.pdf.

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