{"cells": [{"cell_type": "markdown", "metadata": {}, "source": ["# Exercise 8.3: Bootstrapping \"theory\" with hacker stats\n", "\n", "<hr>"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Say we have a data set with $n$ unique measurements. It can be shown that on average a fraction of $(1-1/n)^n$ of the measurements do not appear in a bootstrap sample. 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", "Use hacker stats to show that this 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*!"]}], "metadata": {"anaconda-cloud": {}, "kernelspec": {"display_name": "Python 3", "language": "python", "name": "python3"}, "language_info": {"codemirror_mode": {"name": "ipython", "version": 3}, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.7"}}, "nbformat": 4, "nbformat_minor": 4}