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   "source": [
    "# E9. To be completed after lesson 25\n",
    "\n",
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 9.1\n",
    "\n",
    "Discuss the relationship between these two statements.\n",
    "\n",
    "\\begin{align}\n",
    "&1.\\quad f \\sim \\text{GP}(m(\\mathbf{x}), k(\\mathbf{x}, \\mathbf{x}';\\theta_k)), \\\\[1em]\n",
    "&2.\\quad \\mathbf{f} \\sim \\mathrm{MultiNorm}(\\mathbf{m}(\\mathbf{X}), \\mathsf{K}), \\\\[1em]\n",
    "\\end{align}\n",
    "\n",
    "where the entries in $\\mathsf{K}$ are given by $K_{ij} = k(\\mathbf{x}_i, \\mathbf{x}_j';\\theta_k)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 9.2\n",
    "\n",
    "Are Gaussian processes useful for extrapolation? That is, say we measured $y$ values on an interval $[x_\\mathrm{start}, x_\\mathrm{end}]$. Could we use a Gaussian process to estimate what values of $y$ we might get for $x > x_\\mathrm{end}$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 9.3\n",
    "\n",
    "When we have a GP prior and a Normal likelihood, there are some *really* fortuitous consequences. What are they?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 9.4\n",
    "\n",
    "Did you read the solutions to homework 8?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<br />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 9.5\n",
    "\n",
    "Write down any additional questions you have."
   ]
  }
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