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    "## why is there a n-1 in the formula for the variance?\n",
    "\n",
    "n=5\n",
    "mu=10\n",
    "sigma=2\n",
    "\n",
    "x <- rnorm(n,mean = mu,sd = sigma)\n",
    "plot(seq(1,n,by=1),x)\n",
    "abline(h=mean(x), col='blue')\n",
    "abline(h=mu, col='red')\n",
    "mtext(\"True parameter mu\",col=\"red\",side=3)\n",
    "mtext(\"Sample mean\",col=\"blue\",side=4)\n",
    "\n",
    "\n",
    "# define 3 estimators\n",
    "s1=1/n*sum((x-mu)^2)\n",
    "s2=1/n*sum((x-mean(x))^2)\n",
    "s3=1/(n-1)*sum((x-mean(x))^2)\n",
    "s4=sd(x)^2\n",
    "\n",
    "paste('s1=',s1,'   s2=',s2,'   s3=',s3,'   s4=',s4)"
   ]
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