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    "# Homework 3.2. The Exponential distribution (10 pts)\n",
    "\n",
    "<hr />"
   ]
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   "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",
    "<br />"
   ]
  }
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