diff --git a/lecture_3.ipynb b/lecture_3.ipynb
index 1a39c33b8ecec028014e5e2b66460a05e98b936b..af5da112df4ec58a9ecce86fe420f40beffbb858 100644
--- a/lecture_3.ipynb
+++ b/lecture_3.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "45ae2161",
+   "id": "1c0c65b0",
    "metadata": {},
    "source": [
     "# Lecture 3\n",
@@ -10,9 +10,12 @@
     "---\n",
     "\n",
     "## Parameter estimation\n",
+    "\n",
     "<br>\n",
-    "<br>\n",
     "\n",
+    "Material: [https://gitlab.rrz.uni-hamburg.de/BAN1966/statlecture](https://gitlab.rrz.uni-hamburg.de/BAN1966/statlecture)\n",
+    "\n",
+    "<br>\n",
     " Hartmut Stadie\n",
     "\n",
     "hartmut.stadie@uni-hamburg.de"
@@ -95,7 +98,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fd1987a9",
+   "id": "7be5da9f",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -115,7 +118,7 @@
   {
    "cell_type": "code",
    "execution_count": 47,
-   "id": "1407d2c6",
+   "id": "79dce36a",
    "metadata": {
     "cell_style": "center"
    },
@@ -132,7 +135,7 @@
   {
    "cell_type": "code",
    "execution_count": 49,
-   "id": "1c34c282",
+   "id": "5981183c",
    "metadata": {
     "cell_style": "center",
     "slideshow": {
@@ -178,7 +181,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cc967bb7",
+   "id": "05a58969",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -198,7 +201,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "584b2acc",
+   "id": "4489a6f3",
    "metadata": {},
    "outputs": [],
    "source": []
@@ -231,7 +234,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d221c922",
+   "id": "b4ccd389",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -247,14 +250,17 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b16daf6f",
+   "id": "4c42a0b2",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
     }
    },
    "source": [
-    "## General methods for parameter estimation"
+    "# General methods for parameter estimation\n",
+    "\n",
+    "- method of least squares\n",
+    "- method of maximum likelihood"
    ]
   },
   {
@@ -322,7 +328,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "64e67452-e6bd-442c-a174-e12bdb18dba0",
+   "id": "d283b869",
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -330,15 +336,156 @@
     "tags": []
    },
    "source": [
-    "### Least squares\n",
+    "### Method of least squares\n",
     "\n",
     "$$\\chi^2 = \\sum_i \\left(\\frac{y_i - \\hat y(x)}{\\sigma_i}\\right)^2$$\n",
-    "quantifies the agreement between data and model \n",
+    "quantifies the agreement between data and model "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "64e67452-e6bd-442c-a174-e12bdb18dba0",
+   "metadata": {
+    "cell_style": "split",
+    "slideshow": {
+     "slide_type": "-"
+    },
+    "tags": []
+   },
+   "source": [
     "$\\rightarrow$ $\\hat m$ und $\\hat a$ should $\\chi^2$ minimize.\n",
     "<img src=\"./figures/11/line.png\" style=\"width:80.0%\"\n",
     "alt=\"image\" />"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "id": "ea8ed323",
+   "metadata": {
+    "cell_style": "split"
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "np.float64(6.712257050298824)"
+      ]
+     },
+     "execution_count": 58,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def chi2(x, y, sy, a, m):\n",
+    "    my = m * x + a\n",
+    "    r = (y - my)/sy\n",
+    "    return np.sum(r**2)\n",
+    "\n",
+    "chi2(xs, ys, sigma_y, 1, 2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e34c8317",
+   "metadata": {},
+   "source": [
+    "### Scan $\\chi^2$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 67,
+   "id": "7aa7d079",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from matplotlib import cm\n",
+    "a_mesh, m_mesh = np.meshgrid(np.linspace(-3,5,100), np.linspace(-3,5,100))\n",
+    "chi2_vect = np.vectorize(chi2, excluded=[0, 1])\n",
+    "m_axis = np.linspace(-3,5,100)\n",
+    "\n",
+    "\n",
+    "plt.contourf(a_mesh, m_mesh, chi2_vect(xs, ys, sigma_y, a_mesh, m_mesh), vmin=0, vmax=5000, levels=200, cmap=cm.coolwarm)\n",
+    "plt.xlabel(\"$a$\") \n",
+    "plt.ylabel(\"$m$\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "00e9d884",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "source": [
+    "### Search for minima"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 69,
+   "id": "272e9c69",
+   "metadata": {
+    "cell_style": "split"
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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SaVQa6iQnIiIiunYsMQ7mtp5t0M7PDecqjfhoR4bsOERERNeMJcbBOKmUmDuqfjZm1ZY0lNfUSk5ERER0bVhiHND47m3QoZU7SqtqsXpbhuw4RERE14QlxgGplArMG9URAPDeH2korTJKTkRERNR4LDEOamx0a0TqPFFeU4dVW9JkxyEiImq0RpeYnJwc3H333fDz84Obmxt69OiB5ORky+tCCCxcuBBBQUFwdXXF8OHDceTIkQY/w2AwYM6cOfD394e7uzvGjx+P7OzsBmNKSkoQGxsLrVYLrVaL2NhYlJaWXttd0iWUSgWeGN0JALB6WwYKyw2SExERETVOo0pMSUkJBg0aBLVajZ9++gmpqal444034O3tbRnz2muv4c0338SSJUuwZ88e6HQ63HjjjSgvL7eMmTdvHtavX4/4+Hhs3boVFRUVGDduHEym/23ANmXKFKSkpCAhIQEJCQlISUlBbGzs9d8xWYzqHIDuwd6orjVh2eZTsuMQERE1jmiE+fPni8GDB//l62azWeh0OrF48WLLtZqaGqHVasWKFSuEEEKUlpYKtVot4uPjLWNycnKEUqkUCQkJQgghUlNTBQCxc+dOy5gdO3YIAOLYsWNXlVWv1wsAQq/XN+YWHc4fJwpF6PzvRcQzP4rskirZcYiIyME15v27UTMxGzZsQO/evXHHHXcgICAAPXv2xHvvvWd5PT09Hfn5+Rg9erTlmkajwbBhw7B9+3YAQHJyMmpraxuMCQoKQlRUlGXMjh07oNVq0a9fP8uY/v37Q6vVWsZczGAwoKysrMEX/b1B4X7o394XRpMZ7/52UnYcIiKiq9aoEpOWlobly5cjIiICP//8M2bOnIlHH30UH3/8MQAgPz8fABAYGNjg+wIDAy2v5efnw9nZGT4+PlccExAQcMnvHxAQYBlzsbi4OMv6Ga1Wi+Dg4MbcmsNSKBR46qb6tTFfJmcjvahSciIiIqKr06gSYzab0atXLyxatAg9e/bEQw89hBkzZmD58uUNxikUiga/FkJccu1iF4+53Pgr/ZwFCxZAr9dbvrKysq72thxeTKgvRnRqBZNZ4L+/npAdh4iI6Ko0qsS0bt0aXbp0aXCtc+fOyMzMBADodDoAuGS2pKCgwDI7o9PpYDQaUVJScsUxZ8+eveT3LywsvGSW5wKNRgMvL68GX3T1LjyptOFALo7l86M4IiKyfo0qMYMGDcLx48cbXDtx4gRCQ0MBAGFhYdDpdEhMTLS8bjQakZSUhIEDBwIAYmJioFarG4zJy8vD4cOHLWMGDBgAvV6P3bt3W8bs2rULer3eMoaaVlQbLcZGt4YQwOs/czaGiIisX6NKzGOPPYadO3di0aJFOHXqFNatW4dVq1Zh1qxZAOo/Apo3bx4WLVqE9evX4/Dhw7j33nvh5uaGKVOmAAC0Wi2mT5+OJ554Ar/99hv279+Pu+++G9HR0Rg1ahSA+tmdm2++GTNmzMDOnTuxc+dOzJgxA+PGjUOnTp2a+B8BXfD46I5QKRX49ehZJJ8p+ftvICIikqmxjz5t3LhRREVFCY1GIyIjI8WqVasavG42m8ULL7wgdDqd0Gg0YujQoeLQoUMNxlRXV4vZs2cLX19f4erqKsaNGycyMzMbjCkuLhZTp04Vnp6ewtPTU0ydOlWUlJRcdU4+Yn1t/vnlARE6/3txx4rtwmw2y45DREQOpjHv3wohhJBdpJpDWVkZtFot9Ho918c0Qm5pNYa/vhnGOjPW3NcHwztd+pQYERFRc2nM+zfPTqIGgrxdMW1A/Rqn1xKOw2y2y45LRER2gCWGLvHI8HB4apyQmleGHw7lyY5DRER0WSwxdAkfd2fMGNoeAPDGL8dRazJLTkRERHQplhi6rOmDw+Dn7oyM4ip8sZcbBxIRkfVhiaHLctc4Yc4N4QCAt389iWqj6W++g4iIqGWxxNBfmtwvBG19XFFQbsCH29JlxyEiImqAJYb+ksZJhSfPH0ewYvNpnKs0Sk5ERET0PywxdEXjuwehS2svlBvqsOT3U7LjEBERWbDE0BUplQo8PSYSAPDJzgxknauSnIiIiKgeSwz9raEdW2FwuD9qTQJv/HL877+BiIioBbDE0FW5MBvzbUouDufoJachIiJiiaGrFNVGi/HdgwAAryYck5yGiIiIJYYa4cnRnaBWKfDHySJsPVkkOw4RETk4lhi6aiF+bpjar/5wyEU/HuXhkEREJBVLDDXKoyMjLIdDrt+fIzsOERE5MJYYahRfd2c8MqL+OII3fjmOmloeR0BERHKwxFCj3TeoHYK0LsjV1/A4AiIikoYlhhrNRa3CUzfXH0ewbNNpFFcYJCciIiJHxBJD12RC9zaIauOFCkMd3vntpOw4RETkgFhi6JoolQo8M6YzAODTXZlIK6yQnIiIiBwNSwxds4Hh/rghMgB1ZsEN8IiIqMWxxNB1WTAmEkoF8PORs9iVViw7DhERORCWGLouEYGemNQ3BADwyg/cAI+IiFoOSwxdt8dv7AgPjRMO5ei5AR4REbUYlhi6bv4eGsw6vwHef34+jipjneRERETkCFhiqEncN6gd2vq4Ir+sBu9t4QZ4RETU/FhiqEm4qFV4ekwkAGBF0mnk62skJyIiInvHEkNNZmx0a8SE+qC61oTXfzkuOw4REdk5lhhqMgqFAv8a1wUA8PW+bBzO0UtORERE9owlhppUj2BvTOwRBCGAlzamQgg+ck1ERM2DJYaa3D9vjoSLWondGefw46F82XGIiMhOscRQkwvydsXMYR0AAIt+PIqaWpPkREREZI9YYqhZPDS0A4K0LsgprcZ7W9JkxyEiIjvEEkPNwtVZhadvqT/letlmPnJNRERNjyWGms2t3Vqj9/lHrnnKNRERNTWWGGo2CoUCL9zaFQoFsH5/DvZllsiOREREdoQlhppVdFst/tGrLQDgxY2pPOWaiIiaDEsMNbunbu4Ed2cVDmSV4ut92bLjEBGRnWCJoWYX4OmCR0dGAABeTTiOsppayYmIiMgesMRQi7hvUBja+7ujqMKAd349KTsOERHZAZYYahHOTko8f2v9uUprtmfgVEG55ERERGTrWGKoxQzvFIBRnQNRZxZYuIHnKhER0fVhiaEW9fy4LnB2UmLrqSL8fITnKhER0bVjiaEWFeLnhoeGtgcAvPw9z1UiIqJrxxJDLe6R4eGWc5VWJJ2WHYeIiGwUSwy1OFdnFZ4ZW3+u0vLNp5FZXCU5ERER2SKWGJJibHRrDAr3g6HOjBc3HpEdh4iIbBBLDEmhUCjw4vgoqFUK/HasAL+mnpUdiYiIbAxLDEkTHuCB6YPrF/ku3HiEi3yJiKhRWGJIqkdH1i/yzS6pxrJNp2THISIiG8ISQ1K5OTvhX+Pqd/JdkZSGjKJKyYmIiMhWsMSQdDdH6TAkwh9GkxkLNx7hTr5ERHRVWGJIOoVCgZcmRMFZpcTm44XcyZeIiK4KSwxZhTB/dzx4fiffFzemosJQJzkRERFZO5YYshqzbwhHiK8b8vQ1+G/iCdlxiIjIyrHEkNVwUavw0oSuAIDV2zOQmlsmOREREVkzlhiyKsM7BeCWaB1MZoFnvz0Es5mLfImI6PJYYsjqPD+uK9ydVdifWYr4PVmy4xARkZViiSGro9O64InRnQAAi386iqIKg+RERERkjVhiyCrdMyAUXYO8UFZTh3//cFR2HCIiskIsMWSVnFRK/Pv/oqFQAOv352DrySLZkYiIyMqwxJDV6hHsjXv6hwIAnv32EA+IJCKiBlhiyKo9eVMn6LxccKa4Cu/8dlJ2HCIisiLXVWLi4uKgUCgwb948yzUhBBYuXIigoCC4urpi+PDhOHLkSIPvMxgMmDNnDvz9/eHu7o7x48cjOzu7wZiSkhLExsZCq9VCq9UiNjYWpaWl1xOXbJCnixovnt87ZtWWNBzL594xRERU75pLzJ49e7Bq1Sp069atwfXXXnsNb775JpYsWYI9e/ZAp9PhxhtvRHl5uWXMvHnzsH79esTHx2Pr1q2oqKjAuHHjYDL97+OCKVOmICUlBQkJCUhISEBKSgpiY2OvNS7ZsJu66nBT10DUmQUWfMO9Y4iI6DxxDcrLy0VERIRITEwUw4YNE3PnzhVCCGE2m4VOpxOLFy+2jK2pqRFarVasWLFCCCFEaWmpUKvVIj4+3jImJydHKJVKkZCQIIQQIjU1VQAQO3futIzZsWOHACCOHTt2VRn1er0AIPR6/bXcIlmZvNJq0fX5BBE6/3vx8fZ02XGIiKiZNOb9+5pmYmbNmoWxY8di1KhRDa6np6cjPz8fo0ePtlzTaDQYNmwYtm/fDgBITk5GbW1tgzFBQUGIioqyjNmxYwe0Wi369etnGdO/f39otVrLmIsZDAaUlZU1+CL7odO64J831+8d82rCceTrayQnIiIi2RpdYuLj47Fv3z7ExcVd8lp+fj4AIDAwsMH1wMBAy2v5+flwdnaGj4/PFccEBARc8vMDAgIsYy4WFxdnWT+j1WoRHBzc2FsjKze1Xyh6hnijwlCHf313GELwYyUiIkfWqBKTlZWFuXPnYu3atXBxcfnLcQqFosGvhRCXXLvYxWMuN/5KP2fBggXQ6/WWr6wsbldvb1RKBRbf1g1qlQKJqWfx46HLF1oiInIMjSoxycnJKCgoQExMDJycnODk5ISkpCS88847cHJysszAXDxbUlBQYHlNp9PBaDSipKTkimPOnj17ye9fWFh4ySzPBRqNBl5eXg2+yP500nni4eHhAIAXNhxGSaVRciIiIpKlUSVm5MiROHToEFJSUixfvXv3xtSpU5GSkoL27dtDp9MhMTHR8j1GoxFJSUkYOHAgACAmJgZqtbrBmLy8PBw+fNgyZsCAAdDr9di9e7dlzK5du6DX6y1jyHHNGtEBEQEeKKow4hUeSUBE5LCcGjPY09MTUVFRDa65u7vDz8/Pcn3evHlYtGgRIiIiEBERgUWLFsHNzQ1TpkwBAGi1WkyfPh1PPPEE/Pz84OvriyeffBLR0dGWhcKdO3fGzTffjBkzZmDlypUAgAcffBDjxo1Dp06drvumybZpnFRYfHs3/GPFdny9LxsTegRhaMdWsmMREVELa/Ide//5z39i3rx5eOSRR9C7d2/k5OTgl19+gaenp2XMW2+9hYkTJ+LOO+/EoEGD4Obmho0bN0KlUlnGfPrpp4iOjsbo0aMxevRodOvWDZ988klTxyUbFRPqg3sHtgMALPjmECoNdXIDERFRi1MIO33Eo6ysDFqtFnq9nutj7FSloQ6j39qCnNJq3DuwHRaO7yo7EhERXafGvH/z7CSyWe4aJ8TdFg0A+GhHBvZmnJOciIiIWhJLDNm0oR1b4Y6YthACeOqrgzzpmojIgbDEkM17blwXBHppkF5UiTd+OS47DhERtRCWGLJ5Wle15WOlD7amI/lMyd98BxER2QOWGLILN0QG4rZebWAWwFNfHeDHSkREDoAlhuzG8+O6oJWnBmmFlXjr1xOy4xARUTNjiSG74e3mjEX/V/+x0ntb0rA/kx8rERHZM5YYsis3dgnEhB5BMAvgyS/5sRIRkT1jiSG78+L4rmjlqcHpwkq8/jOfViIislcsMWR3vN2c8ert559W2paOXWnFkhMREVFzYIkhu3RDZCDu6h0MIYAnvzrAs5WIiOwQSwzZrefGdUYbb1dknavGoh+Pyo5DRERNjCWG7Janixr/+Uc3AMCnuzKx5USh5ERERNSUWGLIrg0M98e9A9sBAOZ/fRD6qlq5gYiIqMmwxJDdm39zJML83ZGnr8HzGw7LjkNERE2EJYbsnquzCm/e2R0qpQLfpeRiw4Fc2ZGIiKgJsMSQQ+gZ4oPZI8IBAM+tP4Q8fbXkREREdL1YYshhzL4hHN3balFWU4cnvzwAs1nIjkRERNeBJYYchlqlxJt39YCLWoltp4qxZnuG7EhERHQdWGLIoXRo5YFnx3YBACxOOIYTZ8slJyIiomvFEkMO5+5+IRjeqRWMdWY8+tl+GOp4SCQRkS1iiSGHo1Ao8No/usHX3RnH8svxWgIPiSQiskUsMeSQAjxdLLv5frA1HUnczZeIyOawxJDDGtk5EPcMCAUAPPHFARRVGCQnIiKixmCJIYf2zC2d0THQA0UVBsz/6iCE4GPXRES2giWGHJqLWoW3J/WEs5MSvx0rwCc7z8iOREREV4klhhxe59ZeWDAmEgDwyg9HcSy/THIiIiK6GiwxRADuHdjO8tj17HX7UWWskx2JiMhqmc0C7/52EiWVRqk5WGKIUP/Y9et3dEeApwanCirw4oZU2ZGIiKzW+1vT8EbiCdy2fDtqTWZpOVhiiM7z99Dgv3f1gEIBfL43C9+l5MiORERkdfZlllj215oxpD3UKnlVgiWG6E8GhvtjzvnTrp9dfxhniislJyIish76qlrMWbcfdWaBcd1aY3LfYKl5WGKILvLoyAj0aeeDCkMd5ny2H8Y6eVOlRETWQgiBf359ADml1Qj1c0PcbdFQKBRSM7HEEF3ESaXE25N6QuuqxsFsPV5NOCY7EhGRdB/vOIOfj5yFWqXAksm94Omilh2JJYbocoK8XRscS/DzkXzJiYiI5Dmco8e/fzgKAFgwpjOi22olJ6rHEkP0F0Z31eGBwWEAgCe/PIDM4irJiYiIWl5ZTS1mr9sHo8mMUZ0Dcd+gdrIjWbDEEF3B/DGR6BXijfKaOsxatw+GOpPsSERELUYIgX9+eRAZxVVo4+2K1+/oJn0dzJ+xxBBdgVqlxJIpveDjpsahP02nEhE5gg+3ZSDhSD7UKgWWTu0Fbzdn2ZEaYIkh+htB3q54864eAOoXtm08kCs3EBFRC0g+U4K4H+v/4vbc2C7oEewtN9BlsMQQXYURnQIwa0QHAMCCbw7hdGGF5ERERM3nXKURs9ftQ51ZYGy31rhnQKjsSJfFEkN0lR4b1RH9wnxRYajDw2uTeb4SEdklk1lgbvx+5Olr0N7fHa/ebl3rYP6MJYboKjmplHh3Sk8EeGpw4mwFnv76EIQQsmMRETWpd38/iT9OFsFFrcSyu3vBQ+MkO9JfYokhaoQATxcsndoLTkoFNhzIxUfbM2RHIiJqMpuOFeDt304CAF6ZGI1InZfkRFfGEkPUSH3a+eKZWzoDAF754Sj2ZpyTnIiI6PqdKa7E3Pj9EAK4u38I/hHTVnakv8USQ3QN7hvUDuO6tUadWWDWun0oKK+RHYmI6JpVG02YuXYfymrq0DPEG8+P6yo70lVhiSG6BgqFAq/e3g0RAR44W2bA7HX7UWviQZFEZHuEEHhm/SEczSuDv4czlk+NgbOTbdQD20hJZIXcNU5YERsDD40Tdqef40Z4RGSTPt5xBuv350ClVGDJlF7QaV1kR7pqLDFE16FDKw+8dX4jvDXbM/Dl3iy5gYiIGmFXWjFe/j4VALBgTCT6t/eTnKhxWGKIrtONXQIxd2QEAODZbw/jQFap3EBERFchp7Qaj3xav6Hdrd2DMP38gbe2hCWGqAnMHRmBUZ0DYawz46FPklFYbpAdiYjoL1UbTXjok70orjSia5AXXrPiDe2uhCWGqAkolQq8dVd3dGjljvyyGjzyaTKMdVzoS0TWRwiB+V8fxOGcMvi6O2NlbAxcnVWyY10TlhiiJuLposaqe3rDU+OEPRkleGHDEe7oS0RWZ9WWNGw4kAsnpQLLpvZCWx832ZGuGUsMURPq0MoDb0/uAYUC+Gx3Jj7ecUZ2JCIii83HC/BqwjEAwAu3drG5hbwXY4khamI3RAbi6ZsjAQAvfZ+KrSeLJCciIgJOFZRjzrr9MAtgUp9g3N3fOk+mbgyWGKJm8ODQ9ritVxuYzAKPfJqM9KJK2ZGIyIGVVBox/aO9KDfUoW87X7w4oatNLuS9GEsMUTNQKBRY9H/R6BnijbKaOkz/aA/01bWyYxGRAzLWmTFzbTLOFFch2NcVy+/uBY2TbS7kvRhLDFEzcVGrsDI2Bq21LkgrrMTsdftQx6MJiKgFCSHwwobD2JV+Dh4aJ3wwrQ/8PDSyYzUZlhiiZhTg6YL37ukNV7UKf5wswsKNfGKJiFrOh9sy8NnuLCgVwLuTe6JjoKfsSE2KJYaomUW10eK/k+qfWFq7MxMfbsuQHYmIHMBvR8/i3z/UHynwzC2dMSIyQHKipscSQ9QCbuqqwzNjOgMAXvkhFb+mnpWciIjs2eEcPWb/6UkkWzxS4GqwxBC1kAeGhGFy3xAIATwavx+Hc/SyIxGRHcotrcb9a/agutaEIRH+eHlilF08iXQ5LDFELUShUOClCV0xJMIfVUYTpn+0B3n6atmxiMiOlNfU4v41e1BQbkCnQE8sndoLapX9vtXb750RWSG1SomlU3uhY6AHzpYZcN/qPSiv4aPXRHT96kxmzF63H8fyy9HKU4MP7+sDLxe17FjNiiWGqIV5uajx4b190MpTg2P55Xh47T4eFklE10UIgX99dwRJJwrhqlbhg2m90cbbVXasZscSQyRBWx83rL63D9ydVdh6qghPf32Qj14T0TVb8vspfLY7E0oF8PakHujW1lt2pBbRqBITFxeHPn36wNPTEwEBAZg4cSKOHz/eYIwQAgsXLkRQUBBcXV0xfPhwHDlypMEYg8GAOXPmwN/fH+7u7hg/fjyys7MbjCkpKUFsbCy0Wi20Wi1iY2NRWlp6bXdJZIWi2mix7O4YqJQKfLM/B6//cvzvv4mI6CJf7M3CG4knAAAvTojC6K46yYlaTqNKTFJSEmbNmoWdO3ciMTERdXV1GD16NCor/3cuzGuvvYY333wTS5YswZ49e6DT6XDjjTeivLzcMmbevHlYv3494uPjsXXrVlRUVGDcuHEwmUyWMVOmTEFKSgoSEhKQkJCAlJQUxMbGNsEtE1mPYR1bIe62aADA0k2nsXYnT70moqu36XgBFnxzCAAwa0QHxNrBoY6NIq5DQUGBACCSkpKEEEKYzWah0+nE4sWLLWNqamqEVqsVK1asEEIIUVpaKtRqtYiPj7eMycnJEUqlUiQkJAghhEhNTRUAxM6dOy1jduzYIQCIY8eOXVU2vV4vAAi9Xn89t0jUIt5KPC5C538vwp7+Xvx0KE92HCKyASmZJSLyuZ9E6PzvxWOf7xdms1l2pCbRmPfv61oTo9fX73Ph6+sLAEhPT0d+fj5Gjx5tGaPRaDBs2DBs374dAJCcnIza2toGY4KCghAVFWUZs2PHDmi1WvTr188ypn///tBqtZYxFzMYDCgrK2vwRWQr5o6MwKQ+wTCf30NmZ1qx7EhEZMXSiyote8EM7dgKr97ezW73grmSay4xQgg8/vjjGDx4MKKiogAA+fn5AIDAwMAGYwMDAy2v5efnw9nZGT4+PlccExBw6fbIAQEBljEXi4uLs6yf0Wq1CA4OvtZbI2pxCoUCr0yMwugugTDWmTHjo704ksvN8IjoUvn6Gtz9/i4UVxoR1cYLy+x8L5gruea7nj17Ng4ePIjPPvvsktcuboNCiL9tiBePudz4K/2cBQsWQK/XW76ysrKu5jaIrIaTSol3JvdE3zBflBvqMO3DPcgsrpIdi4isSGmVEfd8uAs5pdUI83fHmvv6wkPjJDuWNNdUYubMmYMNGzZg06ZNaNu2reW6Tle/Ivri2ZKCggLL7IxOp4PRaERJSckVx5w9e+nZMoWFhZfM8lyg0Wjg5eXV4IvI1rioVXh/Wm90bu2FogoDYj/chYLyGtmxiMgKVBnrcN+aPThxtgKBXhp8fH9f+HtoZMeSqlElRgiB2bNn45tvvsHvv/+OsLCGB0qFhYVBp9MhMTHRcs1oNCIpKQkDBw4EAMTExECtVjcYk5eXh8OHD1vGDBgwAHq9Hrt377aM2bVrF/R6vWUMkb3yclHjo/v6INjXFWeKqzDtwz3QV3FXXyJHZqwzY+bafdifWQqtqxqfTO+HYF832bGkUwhx9TtsPfLII1i3bh2+++47dOrUyXJdq9XC1bV+Z8BXX30VcXFxWL16NSIiIrBo0SJs3rwZx48fh6enJwDg4Ycfxvfff481a9bA19cXTz75JIqLi5GcnAyVSgUAGDNmDHJzc7Fy5UoAwIMPPojQ0FBs3LjxqrKWlZVBq9VCr9dzVoZsUkZRJe5YuQOF5Qb0DPHG2un94O7A08ZEjspkFpgbvx/fH8yDq1qFtQ/0Q0yoz99/o41qzPt3o0rMX61HWb16Ne69914A9bM1L774IlauXImSkhL069cPS5cutSz+BYCamho89dRTWLduHaqrqzFy5EgsW7aswWLcc+fO4dFHH8WGDRsAAOPHj8eSJUvg7e19VVlZYsgeHM8vx12rdqC0qhYDO/jhw3v7wEWtkh2LiFqI2Sww/+uD+DI5G2qVAu/d0xvDO1364Is9abYSY0tYYsheHMgqxZT3dqLSaMKozgFYfneMwz6JQORIhBBYuOEIPtpxBkoFsHRKL4yJbi07VrNrzPs3/yQksnLdg73xwb19oHFS4tejBXj8iwMwme3y7x5EdJ4QAq8mHMdHO85AoQBev6O7QxSYxmKJIbIB/dv7YUVsDNQqBTYeyMX8rw/CzCJDZLeW/H4KK5JOAwBemRiF23q1/ZvvcEwsMUQ2YkSnALwzqSdUSgW+Ss7GM+sPscgQ2aFVW05bDnR8bmxnTO3nYOchNQJLDJENGRPdGm/d1QNKBRC/JwvPbzgMO13WRuSQ3v8jDYt+PAYAePzGjnhgSHvJiawbSwyRjRnfPQhv3NkdCgWwdmcmXtyYyiJDZAc+2JqOV344CqD+PLVHR0ZITmT9WGKIbND/9WyLV2/vBgBYsz0Dr/xwlEWGyIat2ZaOl79PBQDMuSEc80axwFwNlhgiG3Vn72As+r9oAPV/g+OMDJFt+nhHBhZurC8ws0Z0wOM3dnTIE6mvBUsMkQ2b0i/EUmTWbM/Av747zMW+RDbkg63peP67IwCAmcM64MnRnVhgGoF7mBPZuCn9QuCkVGD+NwexdmcmTGaBf0+MhlLJPwiJrNnyzafxakL9It6Hh3fAP29igWkslhgiO3Bnn2ColAo89dUBfLY7C3UmgcW3d4OKRYbI6ggh8M5vp/DWr/WPUc8bFYG5IyNYYK4BSwyRnbg9pi2cVAo89nkKvkzOhqHOjDfu7M4jCoisiBACr/9yHEs31W9k99RNnTBrRLjkVLaLJYbIjkzo0QZOSiXmxu/HhgO5qDLWYcmUXjw0ksgKmM0CL/+QitXbMgDUb2THfWCuD/+KRmRnxnZrjffu6W05a2n6R3tQaaiTHYvIodWZzPjn1wctBealCV1ZYJoASwyRHRoRGYA19/WFu7MK204VI/aDXdBX18qOReSQDHUmzFq3D18lZ0OlVOCNO7rjngHtZMeyCywxRHZqQAc/fDqjP7SuauzLLMVdK3egoKxGdiwih1JpqMP0NXvx85GzcFYpsWxqL9wew8McmwpLDJEd6xHsjc8f6g9/Dw2O5Zfj9hXbkV5UKTsWkUM4V2nE1Pd3YeupIrg5q7D6vj64qatOdiy7whJDZOcidV745uGBCPVzQ9a5avxj+XYcytbLjkVk17LOVeEfK7YjJasUWlc1Pn2gHwaF+8uOZXdYYogcQIifG76aORBRbbxQXGnEpFU7sPVkkexYRHYpNbcMty3fjrTCSgRpXfDVzAHoGeIjO5ZdYokhchCtPDX4bEZ/DAr3Q6XRhPvW7MZ3KTmyYxHZle2ni3DXyh0oLDegU6AnvnlkECICPWXHslssMUQOxNNFjQ/v7YNx3Vqj1iQwNz4FSzed4sGRRE1gw4Fc3PvhHpQb6tA3zBdfzBwAndZFdiy7xhJD5GA0Tiq8M6knHhxav0fFf34+jgXfHEKtySw5GZFtEkJgye8n8ehn+2E0mXFLtA4f398XWle17Gh2jyWGyAEplQo8c0tnvDyhK5QKIH5PFqZ/tBflNdxLhqgxjHVmPPXVQbz+S/05SDOGhOHdydwlu6WwxBA5sNgB7bAqtjdc1SpsOVGIO1bsQHZJlexYRDZBX1WLaR/uxlfJ2VAqgJcnRuHZsV148GoLYokhcnCjugQ22Etm4tJtSD5zTnYsIquWUVSJ25Zvw460Yrg7q/DBvX0Q2z9UdiyHwxJDROjW1hvfzR6ELq29UFRhxORVu/B1crbsWERWadupIkxYug2nCyvRWuuCL2cOxIhOAbJjOSSWGCICALTxdsVXDw/ATV0DYTSZ8cSXB7D4p2Mwm/nkEhFQv4B3zbZ03PPhbuira9Ej2BvfzRqELkFesqM5LJYYIrJwc3bC8qkxmHNDOABgRdJpPPDxXh4eSQ7PWGfGgm8OYeHGVJjMArf1aoP4B/sjwIuPUMvEEkNEDSiVCjwxuhPentQDGiclfj9WgAlLtuLE2XLZ0YikOFtWg8nv7UT8niwoFcCzt3TGG3d05xNIVoAlhogua0KPNvj64YFo4+2KjOIqTFy6DT8eypMdi6hF7Uorxth3tiL5TAk8XZzwwbQ+mDG0PRQKPoFkDVhiiOgvRbXRYuOcwRgU7ocqowmPfLoPi386hjpujEd2TgiBD7amY8r7u1BUUX+EwMbZgzEikgt4rQlLDBFdka+7Mz66ry8eOr/D74qk05jy/i6cLauRnIyoeVQY6vBofApe/r5+/cuEHkFYP2sg2vm7y45GF2GJIaK/5aRSYsEtnbF0Si94aJywO/0cxr7zB7ad4knYZF9Sc8sw/t2t2HggF05KBV64tQv+e1cPuDk7yY5Gl8ESQ0RXbWy31tgwexAidZ4oqjDi7g924e1fT8LEx7DJxgkhsG5XJiYu24a0okrovFzw2YP9cd+gMK5/sWIsMUTUKO1beeDbWYMwuW8whADe+vUE7n5/F/L1/HiJbFN5TS0ejU/BM+sPwVhnxohOrfDj3CHo085XdjT6GwohhF3+FaqsrAxarRZ6vR5eXtyIiKg5fLMvG899exhVRhO83dR49fZuuKmrTnYsoqu2L7ME8+JTkHmuCiqlAv+8qRNmDGkPJc8/kqYx798sMUR0XdIKKzA3PgWHcvQAgKn9QvDc2C5wdeYeGmS96kxmLN10Gu/8Xv9xaBtvV7wzuQdiQjn7IhtLDFhiiFqSsc6MN345jpVb0gAA4QEeeOvOHohuq5WcjOhSmcVVeOyLFCSfKQEATOgRhJcmREHrqpacjACWGAAsMUQybD1ZhMe+SEFhuQFOSgVm3xCOWSPCoVZx+R3JJ4TAF3uz8PL3R1FhqIOnxgkvT4zCxJ5tZEejP2GJAUsMkSznKo3417eH8cP53X2j22jx5p3dERHoKTkZObI8fTWe/voQkk4UAgD6tPPBm3f2QLCvm+RkdDGWGLDEEMkkhMDGg3n417eHoa+uhbOTEk/c2BHTB4fBibMy1IKEEPgqORsvfZ+K8po6ODsp8dToTrh/cBhUXLxrlVhiwBJDZA3OltVg/tcHsfl4/d9+o9tosfj2aHQN4loZan7ZJVX417eHsen8f3/dg73xxh3dER7gITkZXQlLDFhiiKyFEAJfJmfjle9TUVZTB5VSgYeGtsejIyN4CjA1C5NZYM32DLzxy3FUGU1wVinx2I0dMWMIZwJtAUsMWGKIrE1BeQ0WbjiCHw/lAwDa+7vj5YlRGBTuLzkZ2ZPU3DI8/c1BHMyuf+S/TzsfxN0WjfAArsmyFSwxYIkhslYJh/Px/HeHUVBuAADc2j0Iz43tjEAvF8nJyJaV19Tiv7+exJrtGTCZBTxdnLBgTGdM6hPMjetsDEsMWGKIrJm+uhZv/nIcn+w8A7MAPDROeOzGjpg2IJTT/dQoQgis35+DRT8eQ1FFfTG+JVqHhbd2RQCLsU1iiQFLDJEtOJyjx3PfHkZKVikAoGOgB/41rguGRLSSG4xswpFcPV747gj2nt+0LszfHQvHd8Wwjvzvx5axxIAlhshWmM0Cn+/NwqsJx1BaVQsAGBkZgGfGdkaHVnyKhC51tqwGb/xyHF8mZ0MIwFWtwpyR4Zg+OAwaJy4Wt3UsMWCJIbI1pVVGvP3bSXyy4wzqzAJOSgViB4Ti0Rsi4OPuLDseWYEqYx1WbUnDyqQ0VNeaAADjurXGM7d0RpC3q+R01FRYYsASQ2SrThVUYNGPR/H7sQIAgKfGCQ8ObY/7B4fBXeMkOR3JUGsy46vkbPz31xM4W1a/7qVniDeeG9sFMaE+ktNRU2OJAUsMka3bcqIQcT8dw9G8MgCAv4cGj44Mx6Q+IXB24uJfR2A2C2w8mIu3Ek8go7gKANDWxxXzb47EuG6toVDwqSN7xBIDlhgie3DhTeyNX04g89z/3sRmjQjH7b3asszYKbNZIPHoWbyVeALH8ssBAH7uznh4eAfc3T+UmyTaOZYYsMQQ2RNjnRmf783CO7+dROH5/WXaeLvi4eEdcEfvtlzMaSdMZoEfD+Vh6aZTlvLi6eKEh4a2x32D+HGio2CJAUsMkT2qNprw2e5MrEg6bdksr7XWBdMHh2FS3xB48E3OJtWazPh2fw6Wbz6NtKJKAPV7B00bGIoHh3SA1k0tOSG1JJYYsMQQ2bOaWhPid2diedJpy0JPLxcnTO0fivsGtuMmZzZCX1WLz/ZkYs22DOSX1QAAtK5q3D8oDPcObMfy4qBYYsASQ+QIampN+GZfDt7/I83yN3hnlRLjewRh2oB2iG7L07KtUWZxFT7clo4v9mahylj/qLS/hwYPDAnD3f1DOaPm4FhiwBJD5EjMZoFfj57Fqi1plt1bgfrHcO8ZEIpboltz3YxkJrPApmMFWLvrDJJOFOLCO0+kzhPTB4dhfI8g/jsiACwxAFhiiBxV8pkSfLwjAz8eykOtqf6PNz93Z/wjpi3u6N2Wpxm3sLNlNfhiTxY+252JXH2N5frQjq0wY0gYBof781FpaoAlBiwxRI6usNyA+N2ZWLc7E3l/evPsGeKNO3sHY1y31vB04ZqL5lBtNOGX1Hx8vS8HW08Wwnz+XcbHTY07egdjSt8QtPN3lxuSrBZLDFhiiKhencmM348V4Iu92dh0vACm8++oGiclRnYOwK3dgjAiMoB7j1ynOpMZO9KK8f2BPPx4KA/lhjrLa33a+WBKvxCMiWrNf870t1hiwBJDRJcqKK/Bt/tz8MXebJwqqLBcd3dWYXRXHW6O0mFIhD/cnLmw9GpcKC4/HsrDz0fO4lyl0fJaWx9X3NarLW7v1Qahfpx1oavHEgOWGCL6a0IIHMktw8aDufj+QB5ySqstr2mclBgc7o8buwTihs4BCPDk49p/VlJpRNKJQvx2rABJxwtQVvO/GRdfd2fcHKXD+O5B6NvOF0ol17pQ47HEgCWGiK6OEAL7Mkvx/cFcJKaeRXZJdYPXI3WeGBLhj0Hh/ugX5gdXZ8f6OMRQZ0JKZim2ny7GtlNF2JdZYlnjAvyvuIyNbo1+Yb5wUvEoCLo+LDFgiSGixhNC4MTZCiSm5iMx9SwOZOsbvO6sUqJ7sBa92/mid6gPYkJ94O3mLClt86gw1OFAVin2Z5ZgV/o57Mk4h5pac4MxkTpPjOwcgBsiA9Ej2BsqzrhQE2KJAUsMEV2/4goDtp8uxtaTRdh6qqjBx04XhAd4ILqNFl2DvNA1SIsuQV7QutrGU08Vhjoczy9Dal45UnP12J9ZiuNny3Hxu4K/hzMGdPDHgPZ+GNapFdp4u8oJTA7BrkrMsmXL8J///Ad5eXno2rUr/vvf/2LIkCF/+30sMUTUlIQQyCiuwp70c9h75hz2nilBWmHlZce28XZF+1bu6NDKAx1auaN9Kw8E+7hBp3Vp8ZO3TWaBgvIapBdVIqOoChnFlUgvqsTx/HLLyeCXy98zxBu9Q30wMNwfEQEe3MuFWozdlJjPP/8csbGxWLZsGQYNGoSVK1fi/fffR2pqKkJCQq74vSwxRNTczlUakZJVgiM5ZTicq8eR3LJL1tT8mUIBtPLQoI2PKwI9XeDr4Qw/d2f4uDnD190Z7honuDmr4OqsgpuzChonFRTnv095vkTUmsww1JlRU2uCoc6MaqMJpdVGlFbVorSqFvrqWhSU1yBfX/9VUG5Anfmv/5gP9NIgUueFzq290CPYG71CvHn2FEllNyWmX79+6NWrF5YvX2651rlzZ0ycOBFxcXENxhoMBhgMBsuvy8rKEBwczBJDRC2qtMqIUwUVOF1YgdOFlThdUIH0okrklFbDUGf++x/QDFRKBYJ9XNHO3x3t/NwR5u+O8AAPROo84eehkZKJ6K80psRY7WYIRqMRycnJePrppxtcHz16NLZv337J+Li4OLz44ostFY+I6LK83ZzrF/62821wXQiBc5VG5JbWIKe0CoXlBhRXGnHu/FdJlREVBhOqjXWoMppQbayfaRFCQAAQAjALAWcnJTROKmiclHBRK+HqrIK3qzO0rmpo3dTQuqoR4KmBzssFOq0LWmtd4e/hzKeGyC5ZbYkpKiqCyWRCYGBgg+uBgYHIz8+/ZPyCBQvw+OOPW359YSaGiMgaKBQK+Hlo4Oeh4enaRE3EakvMBRcvJhNCXHaBmUajgUbDaVEiIiJHYbXzi/7+/lCpVJfMuhQUFFwyO0NERESOx2pLjLOzM2JiYpCYmNjgemJiIgYOHCgpFREREVkLq/446fHHH0dsbCx69+6NAQMGYNWqVcjMzMTMmTNlRyMiIiLJrLrE3HXXXSguLsZLL72EvLw8REVF4ccff0RoaKjsaERERCSZVe8Tcz242R0REZHtacz7t9WuiSEiIiK6EpYYIiIiskksMURERGSTWGKIiIjIJrHEEBERkU1iiSEiIiKbxBJDRERENoklhoiIiGySVe/Yez0u7OFXVlYmOQkRERFdrQvv21ezF6/dlpjy8nIAQHBwsOQkRERE1Fjl5eXQarVXHGO3xw6YzWbk5ubC09MTCoWiSX92WVkZgoODkZWVZZdHGvD+bJ+936O93x9g//fI+7N9zXWPQgiUl5cjKCgISuWVV73Y7UyMUqlE27Ztm/X38PLystv/OAHenz2w93u09/sD7P8eeX+2rznu8e9mYC7gwl4iIiKySSwxREREZJNYYq6BRqPBCy+8AI1GIztKs+D92T57v0d7vz/A/u+R92f7rOEe7XZhLxEREdk3zsQQERGRTWKJISIiIpvEEkNEREQ2iSWGiIiIbBJLzHUaP348QkJC4OLigtatWyM2Nha5ubmyYzWJjIwMTJ8+HWFhYXB1dUWHDh3wwgsvwGg0yo7WpP79739j4MCBcHNzg7e3t+w4123ZsmUICwuDi4sLYmJi8Mcff8iO1GS2bNmCW2+9FUFBQVAoFPj2229lR2pScXFx6NOnDzw9PREQEICJEyfi+PHjsmM1qeXLl6Nbt26WDdIGDBiAn376SXasZhMXFweFQoF58+bJjtIkFi5cCIVC0eBLp9NJy8MSc51GjBiBL774AsePH8fXX3+N06dP4x//+IfsWE3i2LFjMJvNWLlyJY4cOYK33noLK1aswDPPPCM7WpMyGo2444478PDDD8uOct0+//xzzJs3D88++yz279+PIUOGYMyYMcjMzJQdrUlUVlaie/fuWLJkiewozSIpKQmzZs3Czp07kZiYiLq6OowePRqVlZWyozWZtm3bYvHixdi7dy/27t2LG264ARMmTMCRI0dkR2tye/bswapVq9CtWzfZUZpU165dkZeXZ/k6dOiQvDCCmtR3330nFAqFMBqNsqM0i9dee02EhYXJjtEsVq9eLbRarewY16Vv375i5syZDa5FRkaKp59+WlKi5gNArF+/XnaMZlVQUCAAiKSkJNlRmpWPj494//33ZcdoUuXl5SIiIkIkJiaKYcOGiblz58qO1CReeOEF0b17d9kxLDgT04TOnTuHTz/9FAMHDoRarZYdp1no9Xr4+vrKjkGXYTQakZycjNGjRze4Pnr0aGzfvl1SKroeer0eAOz2/3Mmkwnx8fGorKzEgAEDZMdpUrNmzcLYsWMxatQo2VGa3MmTJxEUFISwsDBMmjQJaWlp0rKwxDSB+fPnw93dHX5+fsjMzMR3330nO1KzOH36NN59913MnDlTdhS6jKKiIphMJgQGBja4HhgYiPz8fEmp6FoJIfD4449j8ODBiIqKkh2nSR06dAgeHh7QaDSYOXMm1q9fjy5dusiO1WTi4+Oxb98+xMXFyY7S5Pr164ePP/4YP//8M9577z3k5+dj4MCBKC4ulpKHJeYyLrdw6eKvvXv3WsY/9dRT2L9/P3755ReoVCrcc889EFa8EXJj7w8AcnNzcfPNN+OOO+7AAw88ICn51buWe7QXCoWiwa+FEJdcI+s3e/ZsHDx4EJ999pnsKE2uU6dOSElJwc6dO/Hwww9j2rRpSE1NlR2rSWRlZWHu3LlYu3YtXFxcZMdpcmPGjMHtt9+O6OhojBo1Cj/88AMA4KOPPpKSx0nK72rlZs+ejUmTJl1xTLt27Sz/29/fH/7+/ujYsSM6d+6M4OBg7Ny502qnRxt7f7m5uRgxYgQGDBiAVatWNXO6ptHYe7QH/v7+UKlUl8y6FBQUXDI7Q9Ztzpw52LBhA7Zs2YK2bdvKjtPknJ2dER4eDgDo3bs39uzZg7fffhsrV66UnOz6JScno6CgADExMZZrJpMJW7ZswZIlS2AwGKBSqSQmbFru7u6Ijo7GyZMnpfz+LDGXcaGUXIsLMzAGg6EpIzWpxtxfTk4ORowYgZiYGKxevRpKpW1M3l3Pv0Nb5ezsjJiYGCQmJuL//u//LNcTExMxYcIEicnoagkhMGfOHKxfvx6bN29GWFiY7EgtQghh1X9mNsbIkSMveVrnvvvuQ2RkJObPn29XBQaof687evQohgwZIuX3Z4m5Drt378bu3bsxePBg+Pj4IC0tDc8//zw6dOhgtbMwjZGbm4vhw4cjJCQEr7/+OgoLCy2vydwXoKllZmbi3LlzyMzMhMlkQkpKCgAgPDwcHh4ecsM10uOPP47Y2Fj07t3bMnOWmZlpN+uYKioqcOrUKcuv09PTkZKSAl9fX4SEhEhM1jRmzZqFdevW4bvvvoOnp6dlVk2r1cLV1VVyuqbxzDPPYMyYMQgODkZ5eTni4+OxefNmJCQkyI7WJDw9PS9Zw3RhzaQ9rG168sknceuttyIkJAQFBQV45ZVXUFZWhmnTpskJJPPRKFt38OBBMWLECOHr6ys0Go1o166dmDlzpsjOzpYdrUmsXr1aALjslz2ZNm3aZe9x06ZNsqNdk6VLl4rQ0FDh7OwsevXqZVeP527atOmy/66mTZsmO1qT+Kv/v61evVp2tCZz//33W/77bNWqlRg5cqT45ZdfZMdqVvb0iPVdd90lWrduLdRqtQgKChK33XabOHLkiLQ8CiGseAUqERER0V+wjQUORERERBdhiSEiIiKbxBJDRERENoklhoiIiGwSSwwRERHZJJYYIiIiskksMURERGSTWGKIiIjIJrHEEBERkU1iiSEiIiKbxBJDRERENoklhoisXkZGBhQKBb755hsMHToUrq6uiImJQUZGBjZv3oy+ffvCzc0NI0aMwLlz52THJaIW4iQ7ABHR30lJSQEALFu2DIsWLYKHhwcmTpyI2NhYeHh4YOnSpRBC4JZbbsEHH3yAp556Sm5gImoRLDFEZPUOHDgAHx8fxMfHw9/fHwAwYsQI/P7770hNTYW7uzsAoE+fPsjPz5cZlYhaED9OIiKrl5KSgvHjx1sKDABkZmZi8uTJlgJz4VpYWJiMiEQkAUsMEVm9AwcOoH///g2upaSkoF+/fpZf19TU4MSJE+jRo0cLpyMiWVhiiMiqlZWVISMjAz179rRcO3PmDM6dO9fg2pEjR2AymdC9e3cZMYlIApYYIrJqBw4cgFKpRLdu3SzXUlJS4O3tjXbt2jUY1759e3h6ekpISUQysMQQkVU7cOAAIiMj4erqarm2f//+S2ZcDhw4wI+SiByMQgghZIcgIiIiaizOxBAREZFNYokhIiIim8QSQ0RERDaJJYaIiIhsEksMERER2SSWGCIiIrJJLDFERERkk1hiiIiIyCaxxBAREZFNYokhIiIim8QSQ0RERDbp/wGcZ1F5GjNmigAAAABJRU5ErkJggg==",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.plot(m_axis, chi2_vect(xs, ys, sigma_y, 1, m_axis))\n",
+    "plt.xlabel(\"$m$\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 68,
+   "id": "85f66129",
+   "metadata": {
+    "cell_style": "split"
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.plot(m_axis, chi2_vect(xs, ys, sigma_y, m_axis, 2))\n",
+    "plt.xlabel(\"$a$\")\n",
+    "plt.show()"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "bdc0949d-791e-4e29-9adc-169578e62821",
@@ -349,12 +496,12 @@
     "tags": []
    },
    "source": [
-    "### Methode der kleinsten Quadrate II \n",
+    "### Method of least squares II \n",
     "\n",
-    "Minimiere\n",
+    "Minimize:\n",
     "$\\chi^2 = \\sum_i \\left(\\frac{y_i - \\hat y(x)}{\\sigma_i}\\right)^2 =  \\sum_i \\frac{(y_i - m x_i - a)^2}{\\sigma_i^2}$:\n",
     "\n",
-    "Erste Ableitung ist Null:  \n",
+    "First derivative should be 0:  \n",
     "\n",
     "$$\\begin{aligned}\n",
     "  \\frac{d\\chi^2}{dm} &=& -2\\sum_i  x_i\\frac {y_i -\\hat  m x_i - \\hat a}{\\sigma_i^2} = 0\\\\\n",
@@ -374,14 +521,14 @@
     "tags": []
    },
    "source": [
-    "### Methode der kleinsten Quadrate III \n",
+    "### Method of least squares III \n",
     "\n",
-    "Minimiere\n",
+    "Minimize\n",
     "$\\chi^2 = \\sum_i \\left(\\frac{y_i - \\hat y(x)}{\\sigma_i}\\right)^2 =  \\sum_i \\frac{(y_i - m x_i - a)^2}{\\sigma_i^2}$:  \n",
     "$$\\begin{aligned}\n",
     "    \\sum_i\\frac{x_iy_i}{\\sigma_i^2} - \\hat m \\sum_i\\frac{x_i^2}{\\sigma_i^2}- \\hat a \\sum_i \\frac{x_i}{\\sigma_i^2} &=& 0 \\\\\n",
     "     \\sum_i\\frac{y_i}{\\sigma_i^2} - \\hat m \\sum_i\\frac{x_i}{\\sigma_i^2}- \\hat a \\sum_i \\frac{1}{\\sigma_i^2} &=& 0   \n",
-    "\\end{aligned}$$ mit\n",
+    "\\end{aligned}$$ with\n",
     "$\\frac{1}{\\sum_i 1/\\sigma_i^2} \\sum_i \\frac{f}{\\sigma_i^2} = \\langle f \\rangle$:  \n",
     "$$\\begin{aligned}\n",
     "     \\langle xy  \\rangle -\\langle x^2  \\rangle \\hat m& - \\langle x  \\rangle  \\hat a&= 0\\\\\n",
@@ -399,7 +546,7 @@
     "tags": []
    },
    "source": [
-    "### Methode der kleinsten Quadrate IV \n",
+    "### Method of least squares IV \n",
     "\n",
     "$$\\begin{aligned}\n",
     "       \\hat m&=&\\frac{\\langle xy  \\rangle - \\langle y  \\rangle\\langle x  \\rangle}{\\langle x^2  \\rangle - \\langle x  \\rangle^2} =  \\frac{1}{\\sum_i 1/\\sigma_i^2} \\sum_i \\frac{x_i - \\langle x \\rangle}{\\sigma_i^2(\\langle x^2  \\rangle - \\langle x  \\rangle^2)}y_i\\\\\n",
@@ -408,6 +555,95 @@
     "\\end{aligned}$$"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "ff298bff",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "source": [
+    "### Analytic solution"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 71,
+   "id": "2f96977f",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "13.607587603481903 5.179224444679503 1.9999999999999996 5.629629629629629\n",
+      "1.9937896654845055 1.191645113710492\n"
+     ]
+    }
+   ],
+   "source": [
+    "C = np.eye(n)*sigma_y*sigma_y\n",
+    "W = np.linalg.inv(C)\n",
+    "J = np.ones((len(ys),1))\n",
+    "sum_xy = (np.linalg.inv(J.T@W@J)@(J.T@W@(xs*ys)))[0]\n",
+    "sum_y = (np.linalg.inv(J.T@W@J)@(J.T@W@(ys)))[0]\n",
+    "sum_x = (np.linalg.inv(J.T@W@J)@(J.T@W@(xs)))[0]\n",
+    "sum_x2 = (np.linalg.inv(J.T@W@J)@(J.T@W@(xs*xs)))[0]\n",
+    "print(sum_xy, sum_y, sum_x, sum_x2)\n",
+    "mhat = (sum_xy - sum_x*sum_y)/(sum_x2-sum_x*sum_x)\n",
+    "ahat = (sum_y*sum_x2 - sum_x*sum_xy)/(sum_x2-sum_x*sum_x)\n",
+    "print(mhat, ahat)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ccfc98b3",
+   "metadata": {},
+   "source": [
+    "### Result plot"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 82,
+   "id": "bc2406b4",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x_axis = np.linspace(0,4,100)\n",
+    "plt.errorbar(xs,ys,yerr=sigma_y,fmt=\".\")\n",
+    "plt.plot(x_axis, f(x_axis),'--')\n",
+    "plt.plot(x_axis, x_axis*mhat + ahat,'-')\n",
+    "plt.xlabel(\"x\")\n",
+    "plt.ylabel(\"y\")\n",
+    "plt.savefig(\"line.png\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "510615a5",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "fragment"
+    }
+   },
+   "source": [
+    "Is it good?"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "b08ade05-e5eb-4a7e-9315-31a45c51aadb",
@@ -418,9 +654,8 @@
     "tags": []
    },
    "source": [
-    "## Fehler\n",
-    "\n",
-    "### Fehler \n",
+    "### Errors\n",
+    " \n",
     "\n",
     "$$\\begin{aligned}\n",
     "V(\\hat m) = \\sum_i \\left(\\frac{d\\hat m}{y_i}\\sigma_i\\right)^2\\text{; }\\frac{d\\hat m}{y_i} & = & \\frac{1}{\\sum_i 1/\\sigma_i^2} \\frac{x_i - \\langle x \\rangle}{\\sigma_i^2(\\langle x^2  \\rangle - \\langle x  \\rangle^2)} \\\\\n",
@@ -436,7 +671,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d8828d04-0af8-4dc3-a846-24acbc9a0f8e",
+   "id": "e0843cd2",
    "metadata": {
     "slideshow": {
      "slide_type": ""
@@ -444,7 +679,7 @@
     "tags": []
    },
    "source": [
-    "### Korrelation \n",
+    "### Correlation\n",
     "\n",
     "$$\\begin{aligned}\n",
     "V(\\hat m) &=& \\frac{1}{\\sum_i 1/\\sigma_i^2} \\frac{1}{\\langle x^2  \\rangle - \\langle x  \\rangle^2} \\\\\n",
@@ -452,9 +687,199 @@
     "\\text{cov}(\\hat m, \\hat a) &=&=  \\frac{1}{\\sum_i 1/\\sigma_i^2} \\frac{\\langle (x-\\langle x \\rangle)(\\langle x^2 \\rangle - \\langle x \\rangle x)\\rangle}{(\\langle x^2  \\rangle - \\langle x  \\rangle^2)^2}\\\\\n",
     "&=& \\frac{1}{\\sum_i 1/\\sigma_i^2} \\frac{\\langle x^2 \\rangle \\langle x \\rangle - \\langle x \\rangle \\langle x^2 \\rangle - \\langle x \\rangle \\langle x^2 \\rangle + \\langle x \\rangle^2\\langle x \\rangle}{(\\langle x^2  \\rangle - \\langle x  \\rangle^2)^2}\\\\\n",
     "&=& - \\frac{1}{\\sum_i 1/\\sigma_i^2} \\frac{\\langle x \\rangle}{\\langle x^2  \\rangle - \\langle x  \\rangle^2}\n",
-    "\\end{aligned}$$\n",
+    "\\end{aligned}$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d8828d04-0af8-4dc3-a846-24acbc9a0f8e",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    },
+    "tags": []
+   },
+   "source": [
+    "### Errors from analytical expression"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 72,
+   "id": "81650a70",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 0.00981818 -0.01963636]\n",
+      " [-0.01963636  0.05527273]]\n",
+      "0.09908673886137244 0.2351015254581034 -0.8429272304235245\n"
+     ]
+    }
+   ],
+   "source": [
+    "sum_siginv = sigma_y*sigma_y/len(ys)\n",
+    "V_am = np.array([[sum_siginv/(sum_x2-sum_x*sum_x), -sum_siginv*sum_x/(sum_x2-sum_x*sum_x)],\n",
+    "                 [-sum_siginv*sum_x/(sum_x2-sum_x*sum_x), sum_siginv*sum_x2/(sum_x2-sum_x*sum_x)]])\n",
+    "print(V_am)\n",
+    "print(np.sqrt(V_am[0,0]), np.sqrt(V_am[1,1]), V_am[1,0]/(np.sqrt(V_am[0,0])*np.sqrt(V_am[1,1])))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b914474b",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "source": [
+    "### Covariance directly from C\n",
+    "$$\\frac{d\\hat m}{y_i} =  \\frac{1}{\\sum_i 1/\\sigma_i^2} \\frac{x_i - \\langle x \\rangle}{\\sigma_i^2(\\langle x^2  \\rangle - \\langle x  \\rangle^2)}$$\n",
     "\n",
-    "### Beispiel in Jupyter "
+    "$$\\frac{d\\hat a}{y_i} =   \\frac{1}{\\sum_i 1/\\sigma_i^2} \\frac{\\langle x^2 \\rangle - \\langle x \\rangle x_i}{\\sigma_i^2(\\langle x^2  \\rangle - \\langle x  \\rangle^2)}$$\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 78,
+   "id": "320c4340",
+   "metadata": {
+    "cell_style": "split"
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[-0.12272727 -0.09545455 -0.06818182 -0.04090909 -0.01363636  0.01363636\n",
+      "   0.04090909  0.06818182  0.09545455  0.12272727]\n",
+      " [ 0.34545455  0.29090909  0.23636364  0.18181818  0.12727273  0.07272727\n",
+      "   0.01818182 -0.03636364 -0.09090909 -0.14545455]]\n",
+      "[[0.16 0.   0.   0.   0.   0.   0.   0.   0.   0.  ]\n",
+      " [0.   0.16 0.   0.   0.   0.   0.   0.   0.   0.  ]\n",
+      " [0.   0.   0.16 0.   0.   0.   0.   0.   0.   0.  ]\n",
+      " [0.   0.   0.   0.16 0.   0.   0.   0.   0.   0.  ]\n",
+      " [0.   0.   0.   0.   0.16 0.   0.   0.   0.   0.  ]\n",
+      " [0.   0.   0.   0.   0.   0.16 0.   0.   0.   0.  ]\n",
+      " [0.   0.   0.   0.   0.   0.   0.16 0.   0.   0.  ]\n",
+      " [0.   0.   0.   0.   0.   0.   0.   0.16 0.   0.  ]\n",
+      " [0.   0.   0.   0.   0.   0.   0.   0.   0.16 0.  ]\n",
+      " [0.   0.   0.   0.   0.   0.   0.   0.   0.   0.16]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "dmdy = sum_siginv / (sum_x2-sum_x*sum_x)*(xs-sum_x)/sigma_y**2\n",
+    "dady = sum_siginv / (sum_x2-sum_x*sum_x)*(sum_x2-xs*sum_x)/sigma_y**2\n",
+    "A=np.array([dmdy,dady])\n",
+    "print(A)\n",
+    "print(C)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 79,
+   "id": "14ef3529",
+   "metadata": {
+    "cell_style": "split"
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 0.00981818 -0.01963636]\n",
+      " [-0.01963636  0.05527273]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "C_am = A@C@A.T\n",
+    "print(C_am)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2dbb774c",
+   "metadata": {},
+   "source": [
+    "### Error band for fitted line\n",
+    "\n",
+    "$y = \\hat m x +\\hat a$ \n",
+    "\n",
+    "$\\frac{dy}{dm} = x$ und $\\frac{dy}{da} = 1$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 88,
+   "id": "f507dabf",
+   "metadata": {
+    "cell_style": "split"
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.09908673886137244 0.2351015254581034\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "np.float64(0.12649110640673517)"
+      ]
+     },
+     "execution_count": 88,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def err(x, V):\n",
+    "    A = np.array([x, 1])\n",
+    "    return np.sqrt(A.T@V@A)\n",
+    "\n",
+    "print(np.sqrt(V_am[0,0]), np.sqrt(V_am[1,1]))\n",
+    "err(0, V_am)\n",
+    "err(2, V_am)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 89,
+   "id": "85d872e5",
+   "metadata": {
+    "cell_style": "split"
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x_axis = np.linspace(-2,6,100)\n",
+    "plt.errorbar(xs,ys,yerr=sigma_y,fmt=\".\")\n",
+    "plt.plot(x_axis, f(x_axis),'--')\n",
+    "plt.plot(x_axis, x_axis*mhat + ahat,'-g')\n",
+    "plt.plot(x_axis, x_axis*mhat + ahat - np.vectorize(err,excluded=[1])(x_axis, V_am),'--g')\n",
+    "plt.plot(x_axis, x_axis*mhat + ahat + np.vectorize(err,excluded=[1])(x_axis, V_am),'--g')\n",
+    "\n",
+    "plt.xlabel(\"x\")\n",
+    "plt.ylabel(\"y\")\n",
+    "plt.savefig(\"line.png\")\n",
+    "plt.show()"
    ]
   },
   {
@@ -467,7 +892,7 @@
     "tags": []
    },
    "source": [
-    "### Minimales $\\chi^2$ \n",
+    "### Minimal $\\chi^2$ \n",
     "\n",
     "$$\\begin{aligned}\n",
     "  \\chi^2 &=& \\sum_i \\frac{(y_i - \\hat m x_i - \\hat a)^2}{\\sigma_i^2} = \\sum_i \\frac{\\left[y_i -  \\frac{\\langle xy  \\rangle - \\langle y  \\rangle\\langle x  \\rangle}{\\langle x^2  \\rangle - \\langle x  \\rangle^2} x_i - \\frac{ \\langle y \\rangle \\langle x^2 \\rangle -  \\langle x \\rangle \\langle xy \\rangle}{ \\langle x^2 \\rangle -  \\langle x \\rangle^2} \\right]^2}{\\sigma_i^2}\\\\\n",
@@ -679,7 +1104,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "70701265",
+   "id": "43536528",
    "metadata": {},
    "outputs": [],
    "source": []