set.seed(421)     # for reproducibility
m = 20000;  n = 5
par(mfrow=c(1,3))
x = rnorm(m*n); DTA = matrix(x, nrow=m)
 a = rowMeans(DTA);  s = apply(DTA, 1, sd)
 plot(a, s, pch=".", main="Standard Normal")
 cor(a,s)
 [1] -0.001354763    # consistent with 0
x = rexp(m*n); DTA = matrix(x, nrow=m)
 a = rowMeans(DTA);  s = apply(DTA, 1, sd)
 plot(a, s, pch=".", main="Standard Exponential")
 cor(a,s)
 [1] 0.7695967
x = rbeta(m*n, .1,.1); DTA = matrix(x, nrow=m)
 a = rowMeans(DTA);  s = apply(DTA, 1, sd)
 plot(a, s, pch=".", main="Standard Normal")
 cor(a,s)
 [1] -0.008673277   # consistent with 0
par(mfrow=c(1,1))

set.seed(2019)
m = 10^4    # for good graph, don't use too many
            # for accurate est of r, use very many
x = runif(m);  x1 = (x<.3);  x2 = (x>=.8)
cor(x1, x2)
[1] -0.327649
jit1 = runif(m, -.25, .25); jit2 = runif(m, -.25, .25)
 plot(x1+jit1, x2+jit2, pch=".")