Sum of roll of N dice

[Dieter]

(05-06-2018 08:18 PM)zooropa1844 Wrote:  Dieter, how did you get the general formula for the variance n*35/12? I just checked its exactness for the cases n=3, 4 and 5.

A single (fair) die follows a discrete uniform distribution where the random variable can be anything in {1, 2, 3, 4, 5, 6}. Here the mean µ is (1+6)/2=3,5 and the variance σ² is [(1–3,5)²+(2–3,5)²+...+(6–3,5)²]/6 = 17,5/6 = 35/12. Or, according to the formula on the linked Wikipedia page, [(6–1+1)²–1]/12 = 35/12.

The sum of n equal, uniformly distributed random variables, i.e. the sum of n dice rolls, then simply is n times the individual variance, i.e. n·σ² or n·35/12.

Dieter