{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Homework 3.2. The Exponential distribution (10 pts)\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"*You may submit this problem as a PDF, either with clearly typed mathematics or with neat handwriting, if you like.*\n",
"\n",
"Say I am interested in modeling the time it between repressor-operator binding events in a cell. We might model the time $t$ to be Exponentially distributed, having probability density function\n",
"\n",
"\\begin{align}\n",
"f(t;\\beta) = \\beta \\mathrm{e}^{-\\beta t}.\n",
"\\end{align}\n",
"\n",
"**a)** Why might we model $t$ as being Exponentially distributed?\n",
"\n",
"**b)** Write down the CDF, $F(t;\\beta)$.\n",
"\n",
"**c)** Say you are interested instead in the reciprocal time, $k = 1/t$. Write down the PDF for $k$, $f(k;\\beta)$.\n",
"\n",
" "
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.11.5"
}
},
"nbformat": 4,
"nbformat_minor": 4
}