Discrete uniform random variable having variance 1

Question

I would like to plot in R a discrete uniform random variable having variance 1, with an interval of [-a,a].

I have tried using Var(X)= (n^2-1)/12

Then getting that n should be n = sqrt(13)
Plugging this into

n=b-a+1=a-(-a)+1
a=(sqrt(13)-1)/2 = 1.302776

Trying this in R with the code

X <- sample(-1.302276:1.30227,1000, replace=TRUE)

The variance becomes around 0.65

Answer 1

The variance of a uniform distribution between a and b is (b - a) * (b - a) / 12 .

Therefore, for the interval [-a, +a] to have a variance of 1, you need to set

a = sqrt(3)