n <- 10000
u <- runif(n,0,1)


running.mean <- rep(0,n)
for (i in 1:n) running.mean[i] <- mean(u[1:i])
plot(1:n,running.mean,type="l")

n <- 100000
u <- rcauchy(n,0,1)

running.mean <- rep(0,n)
for (i in 1:n) running.mean[i] <- mean(u[1:i])
plot(1:n,running.mean,type="l")