具有方差1的离散均匀随机变量

Question

I would like to plot in R a discrete uniform random variable having variance 1, with an interval of [-a,a]. 我想在R中绘制一个方差为1且间隔为[-a，a]的离散均匀随机变量。

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

Then getting that n should be n = sqrt(13) 然后得到n应该是n = sqrt(13)
Plugging this into 将其插入

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

Trying this in R with the code 用代码在R中尝试

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

The variance becomes around 0.65 方差约为0.65

Answer 1

The variance of a uniform distribution between a and b is (b - a) * (b - a) / 12 . a和b之间的均匀分布的方差为(b - a) * (b - a) / 12 。

Therefore, for the interval [-a, +a] to have a variance of 1, you need to set 因此，对于间隔[-a, +a]的方差为1，您需要设置

a = sqrt(3)