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   "source": [
    "# Lesson 9 exercises\n",
    "\n",
    "<hr />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 9.1\n",
    "\n",
    "What is the relationship between a cumulative distribution function (CDF) and a probability density function (PDF)? We didn't cover it in class, but what is the relationship between as CDF and a probability mass function (PMF)?"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br />"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 9.2\n",
    "\n",
    "Say I am interested in modeling the time it takes for a certain process to happen in a cell. For reasons that you will understand in future lessons, we might model the time $t$ to be Exponentially distributed, having probability density function\n",
    "\n",
    "\\begin{align}\n",
    "f(t) = \\beta \\mathrm{e}^{-\\beta t}.\n",
    "\\end{align}\n",
    "\n",
    "1. Write down the CDF, $F(t)$.\n",
    "2. Say you are interested instead in the reciprocal time, $k = 1/t$. Write down the PDF for $k$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 9.3\n",
    "\n",
    "Write down any questions or points of confusion that you have."
   ]
  }
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