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    "# Homework 6.3: Bootstrapping theory with... bootstrapping! (15 pts)\n",
    "\n",
    "<hr>"
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    "Say we have a data set with $n$ unique measurements. \n",
    "\n",
    "\n",
    "**a)** Show that on average a fraction of $(1 - 1/n)^n$ of the measurements do not appear in a bootstrap sample. Note that for large $n$, this is approximately  $1/\\mathrm{e} \\approx 1/2.7$, since $\\lim_{n\\to\\infty}(1 - 1/n)^n =  1/\\mathrm{e}$. This part of the problem is optional and not graded.\n",
    "\n",
    "**b)** Use a bootstrapping approach to demonstrate that this is indeed true. Hint: Think about a convenient \"data set\" to use for drawing samples. This is kind of fun; you're investigating some theory behind bootstrapping with bootstrapping!"
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    "<hr>"
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