#--- Law of Large Number ---
 
  X <- rnorm(2000, 3, 4)
  
  A <- cumsum(X)/(1:2000)

  plot(A, type="l")
  abline(h=3, col="red")












#--- Central Limit Theorem ---

#- Uniform  -------
  n <- 3
  
  record <- 0
  for (i in 1:10000) {
  
    X <- runif(n, 0, 1)
  
    Xbar <- mean(X)
    record[i] <- print(Xbar)
  
  }
  
  plot(ecdf(record))
  t <- seq(-5,5,.1)
  lines(t, pnorm(t, .5, sqrt(1/12/n)), col='red')




#--- Exp CLT -----------
  n <- 50
  
  record <- 0
  for (i in 1:10000) {
  
    X <- rexp(n, 1)
  
    Xbar <- mean(X)
    record[i] <- print(Xbar)
  
  }
  
  plot(ecdf(record))
  t <- seq(-5,5,.01)
  lines(t, pnorm(t, 1, sqrt(1/n)), col='red')