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    "# Homework 6.1: Bootstrapping \"theory\" with hacker stats [25 pts]\n",
    "\n",
    "<hr>"
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    "Say we have a data set with $n$ unique measurements. \n",
    "\n",
    "**a)** Show that on average a fraction of $(1-1/n)^n$ of the measurements do not appear in a bootstrap sample. \n",
    "\n",
    "Note that for large samples, this is approximately $1/e \\approx 1/2.7$, since\n",
    "\n",
    "\\begin{align}\n",
    "\\lim_{n\\to\\infty} (1-1/n)^n = 1/e.\n",
    "\\end{align}\n",
    "\n",
    "**b)** Use hacker stats to demonstrate that the result you derived in is indeed true. *Hint*: Think about a convenient \"data set\" to use for drawing samples.\n",
    "\n",
    "This is kind of fun; you're investigating some theory behind hacker stats *with hacker stats*! If you couldn't solve part (a), you could still make a plot using results from part (b) and get the basic idea."
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