diff --git a/1_data_science/0_zufallszahlenlabor/main.ipynb b/1_data_science/0_zufallszahlenlabor/main.ipynb
index 1b2d4ac..beaa849 100644
--- a/1_data_science/0_zufallszahlenlabor/main.ipynb
+++ b/1_data_science/0_zufallszahlenlabor/main.ipynb
@@ -593,12 +593,85 @@
     "print(f\"Korrelation der erzeugten Zufallszahlenpaare: {korrelation:.4f}\")"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 3. Modellierung der abhangigen Variablen in der Simulationsstudie"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Varianz der Residuen (β0=0, β1=0): 0.2500\n",
+      "Varianz der Residuen (β0=-500, β1=1000): 0.0013\n",
+      "Varianz der Residuen (β0=-3, β1=6): 0.1496\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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katasqenTp2vhwoWSrhx3brNvf/zxhyTHK5yqVq2q4ODgG+Z1dWGRfW7yeo/cZs0Kws3NTQ8++KAkqV+/furcubPGjh2roUOH5rvIz3bnnXfqrrvuylfs1bc7FuQcSrI3JbN/twAAtwbqJWvqpREjRmjevHlavny5hg4dqnnz5ik4OFgPP/xwgfPNzuvqCcFreXt7KyIiQhERERo4cKDuvvtujR071t6U8vPzU3p6ui5cuKCyZcs6vPaPP/5QWFiY/bmvr2+BajlJqlChgmw2W4FqiYJq2bKlWrZsqUcffVQ1a9bUhAkT9Pzzz6tNmzYF3ld+a6Wr61M/Pz8lJCTkiDl//rwyMzNzPT4PDw9qJRQ7mlKAk/D09NQTTzyhRYsW6cSJE3r33Xfl7e3tsPi1v7+/mjRpoilTpuS6j4JcOXKt7Ct9xo0bp969e+cac+3ilDfi7u6ujIyMHOOFvfw5u5A6efKkqlSpYh+/dOlSgfaZmJiY65ibm5vD+gX54e/vr8zMTJ0/fz7XS8qvVbVqVYWEhDgsSNq4cWOtXLnSYY0mSfaFXBs1amQfK8zte9mv3717t7p27eoQt3v3bof93yybzaY2bdpo/fr1SklJue4VZLkp7O17jRs3znXh29zOofS/ArOg+QEAShb10o0VRb1Uu3ZtdenSRfPnz1eXLl20evVqTZo0qUBXk2fLPmfZn7034ubmphYtWujDDz+0j2Xfar979261atXKPp6YmKjTp087fM4X5vY9T09P1a5dO89awtPTM9elFgrr3nvvlaQcC9TnV2Fu32vcuLFWrVplv80zW161knTlZ5ZdawHFhaYU4EQGDRqkBQsWaObMmVq3bp369+/vMBvUrVs3rVu3TrVq1VKFChUK9R7XzqZlq1u3rkJDQ/XDDz9o6tSphT+Iq1SvXl0//vijw9jGjRt17ty5Qu3v/vvvlyR98MEHDusSfPTRRwX6RpRPPvlEM2fOtM/YnT17VmvWrNF9991X4GKrXr16kpTn4pjXLop5+vRpHT9+3OHS+169emnRokX6+OOP9fjjj9vHly1bpqCgIIfiqzC371WpUkUtW7ZUdHS0xowZYz/G7du368CBAxo1alT+DjYXp0+f1tmzZx3e74cfflC5cuUK1fAp7O17vXr10rBhw7Rjxw77+cq+paNVq1Y5/gck++dS2AXZAQAlh3rp+oqqXnr++efVsWNH+wLyuS0Snx/ZtzLm9S1uR48ezTEx9+OPPzosc9C5c2d5eHho6dKlDnVR9jqWV9/mV9jb93r16qXZs2fr6NGj9vWezp49q08++UQ9evTI8YU0BXHw4EGHuuiHH36QJIdjLIjC3L738MMPa8KECVq2bJn++te/2seXLl0qT09Pde7c2eG1ly5d0tGjR3NMaAJFjaYU4ESaN2+uJk2aaPbs2TLGaNCgQQ7bX331VcXFxalNmzYaOXKk6tatq/T0dB0+fFjr1q3TggULbnhrV61ateTp6anly5erfv36uvPOOxUUFKSgoCC988476tKlizp16qT+/furSpUq+uOPP7R//3599913DjNW+REZGamXX35Zr7zyitq2bat9+/Zp3rx5Bb6kOlvDhg31xBNP6O9//7vKlCmjBx98UHv37tXf//53+fj45HtR0TJlyigiIkIvvPCCLl++rOnTpys1NdW+GHlBtGvXTtKVBk9uTam3335bly5dUp8+fXT+/HnNnDlTkvTMM8/YY7p06aKIiAj9+c9/VmpqqmrXrq2VK1cqNjZW0dHRDo2y6tWrF2rGavr06YqIiNBjjz2mYcOGKSkpSS+99JIaNWqUYzYxe/+HDx++4X5Pnjyp+++/Xy+99JL8/f21fv16ffrppxo/frxD3L59+7Rv3z5JV2Y1L1y4oI8++kjSlcZQdnPI29tbzZs3L/DxDRw4UPPnz9djjz2m1157TQEBAXrrrbd04MABbdiwIUf89u3bVaZMGXvhDgC4dVAvXV9R1UsRERFq0KCBNm3apKeeeuq6a0JdT3BwsGrWrKnt27dr5MiRObb/+OOPioiI0KhRo1S2bFmtWrVK3333nf7xj3/YY3x9fTVhwgS9/PLL8vX1VceOHbVr1y5FRUVp8ODBDpNMfn5+BVrWIduYMWP0/vvv66GHHtKrr74qd3d3vfbaa0pPT8+x8Hr//v21bNkyh6u2r6dbt26aOHGiGjVqpN27d2vixIm67777HG7DO3XqlH09sOyrl7744gtVrFhRFStWVNu2be2xhamVGjZsqEGDBmnixIkqU6aMWrRoofXr12vhwoWaPHlyjtv3fvzxR124cCHfV7ADhWYAOJU333zTSDINGjTIdfupU6fMyJEjTY0aNYyrq6vx9fU1YWFhZvz48ebcuXPGGGMOHTpkJJmZM2fmuo+VK1eaevXqGVdXVyPJTJw40b7thx9+MH369DEBAQHG1dXVBAYGmgcffNAsWLDAHrNp0yYjyWzatMk+NnHiRHPtPykZGRlm7NixJiQkxHh6epq2bduahIQEU61aNdOvXz973JIlS4wks2vXLofX5/Y+6enp5oUXXjABAQHGw8PDtG7d2mzbts34+PiYv/zlL9c7tfbzMn36dDNp0iQTHBxs3NzcTLNmzcyXX37pEJud06FDh667T2OMue+++0zXrl1zfa/u3bubsLAwc+edd5qKFSuaBx980Hz99dc59nH27FkzcuRIExgYaNzc3EyTJk3MypUrb/jeBbF+/XrTunVr4+HhYXx9fc3TTz9tTp48mSPO39/ftG7d+ob7a9u2rQkODjaPP/64CQgIMGXLljUNGzY0r7/+usnMzHSIzf79yO1x9e/fzUhMTDRPP/208fX1tf9uxMXF5Rp73333me7duxfJ+wIArEe99D9FXS9dLSoqykgy27dvz7Et+/wtWbLkhvt5+eWXTYUKFUx6errDeLVq1UzTpk1N165dja+vr/H29jbNmjUz7777rrl8+XKO/bz55pumTp06xs3NzVStWtVMnDgxR81xM37++WfTs2dPU65cOVO2bFnTvn17Ex8fnyPukUceMZ6eniY5Ofm6+8v+eQ8bNsxUrVrVuLu7m5o1a5o///nP5tSpUw6x2T/H3B5t27YtkuPLzMw0EydONFWrVjVubm6mTp06Zs6cObnGvvzyy8bf3z/HzwwoajZj/u9GWgC4RW3dulX33HOPli9frr59++YZd/jwYdWoUUMzZ87Mc3HSwsi+7e7XX3+1r91QXO9V3Pbt26eGDRtq7dq1euihh64b265dO50+fVp79uyxKLui8csvvyg0NFRffvmlIiIiSjodAAAskd966WrNmzeXzWYr9LfZZTt+/Lhq1Kih9957z2GpgurVq6tRo0Zau3btTe3faoGBgYqMjLRfAZ+XqKgoTZo0SadOnbql1rHMyspS7dq11bdv3zzXZgOKCrfvAbilxMXFadu2bQoLC5Onp6d++OEHvfbaawoNDc1zwdHi1rt3b7Vo0ULTpk3TvHnzSiSHorJp0yaFh4ffsCF1K5s8ebLat29PQwoAcNu6mXopNTVVe/bs0dq1axUfH6+YmJibzicoKEijRo3SlClT9Nhjj+X7FkJntHfvXl24cMFhXabbTXR0tM6dO6cXX3yxpFNBKUBTCsAtpVy5clq/fr1mz56ts2fPyt/fX126dNG0adOu+1XDxclms2nRokVavXq1Ll++fEsXWsOHD9fw4cNLOo1ic+nSJdWqVUvjxo0r6VQAACg2N1Mvfffdd3rggQfk5+eniRMnOiwifjMmTJigsmXL6rfffrMvJH4ratiwoVJTU0s6jWJ1+fJlLV++XOXLly/pVFAKcPseAAAAAAAALHfrTucDAAAAAADglkVTCgAAAAAAAJajKQUAAAAAAADLsdB5Ebp8+bKOHz8ub29v2Wy2kk4HAAAUA2OMzp49q6CgoFv6iw1KCvUSAAC3v/zWSzSlitDx48dv6W+SAAAA+Xf06FEFBweXdBq3HOolAABKjxvVSzSlipC3t7ekKye9XLlyJZwNAAAoDqmpqQoJCbF/7qNgqJcAALj95bdeoilVhLIvQS9XrhxFFgAAtzluPSsc6iUAAEqPG9VLLIQAAAAAAAAAy9GUAgAAAAAAgOVoSgEAAAAAAMByNKUAAAAAAABgOZpSAAAAAAAAsBxNKQAAAAAAAFiOphQAAAAAAAAsR1MKAAAAAAAAlivRptS//vUvde/eXUFBQbLZbPr0008dthtjFBUVpaCgIHl6eqpdu3bau3evQ0xGRoZGjBghf39/eXl5qUePHjp27JhDTHJysiIjI+Xj4yMfHx9FRkbqzJkzDjFHjhxR9+7d5eXlJX9/f40cOVKZmZnFcdgAAAAAAAClXok2pc6fP6+mTZtq3rx5uW6fMWOG3njjDc2bN0+7du1SYGCgIiIidPbsWXvMqFGjFBMTo1WrVumbb77RuXPn1K1bN2VlZdlj+vbtq4SEBMXGxio2NlYJCQmKjIy0b8/KytJDDz2k8+fP65tvvtGqVav08ccfa/To0cV38AAAAEUkKipKNpvN4REYGGjfbuVEHwAAQH7ZjDGmpJOQJJvNppiYGPXs2VPSleIpKChIo0aN0l//+ldJV4qlSpUqafr06XrmmWeUkpKiihUr6v3339fjjz8uSTp+/LhCQkK0bt06derUSfv371eDBg20fft2tWrVSpK0fft2hYeH6z//+Y/q1q2rL774Qt26ddPRo0cVFBQkSVq1apX69++vpKQklStXLl/HkJqaKh8fH6WkpOT7NQAA4NbijJ/3UVFR+uijj7Rhwwb7WJkyZVSxYkVJ0vTp0zVlyhQtXbpUderU0eTJk/Wvf/1LBw4ckLe3tyTpz3/+s9asWaOlS5fKz89Po0eP1h9//KH4+HiVKVNGktSlSxcdO3ZMCxculCQNHTpU1atX15o1a/KdqzOePwAAULTy+3nvYmFOBXLo0CElJiaqY8eO9jF3d3e1bdtWW7du1TPPPKP4+Hh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+      "text/plain": [
+       "<Figure size 1200x1200 with 6 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from scipy.special import expit as sigmoid\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "# Parameter\n",
+    "anzahl_elemente = 10_000\n",
+    "parameter_sets = [\n",
+    "    (0, 0),\n",
+    "    (-500, 1000),\n",
+    "    (-3, 6)\n",
+    "]\n",
+    "\n",
+    "xi = np.random.uniform(0, 1, anzahl_elemente)\n",
+    "\n",
+    "results = []\n",
+    "\n",
+    "for beta_0, beta_1 in parameter_sets:\n",
+    "    pi = sigmoid(beta_0 + beta_1 * xi)\n",
+    "    yi = np.random.binomial(1, pi)\n",
+    "    residuen = yi - pi\n",
+    "    results.append({\n",
+    "        'beta_0': beta_0,\n",
+    "        'beta_1': beta_1,\n",
+    "        'pi': pi,\n",
+    "        'yi': yi,\n",
+    "        'residuen': residuen,\n",
+    "        'varianz_residuen': np.var(residuen)\n",
+    "    })\n",
+    "\n",
+    "fig, axes = plt.subplots(3, 2, figsize=(12, 12))\n",
+    "for i, res in enumerate(results):\n",
+    "    axes[i, 0].hist(res['pi'], bins=50, color='skyblue', edgecolor='black')\n",
+    "    axes[i, 0].set_title(f'Verteilung pi (β0={res[\"beta_0\"]}, β1={res[\"beta_1\"]})')\n",
+    "    axes[i, 0].set_xlabel('pi')\n",
+    "    axes[i, 0].set_ylabel('Häufigkeit')\n",
+    "    \n",
+    "    axes[i, 1].hist(res['yi'], bins=2, color='orange', edgecolor='black', rwidth=0.8)\n",
+    "    axes[i, 1].set_title(f'Verteilung yi (β0={res[\"beta_0\"]}, β1={res[\"beta_1\"]})')\n",
+    "    axes[i, 1].set_xlabel('yi')\n",
+    "    axes[i, 1].set_ylabel('Häufigkeit')\n",
+    "    \n",
+    "    print(f\"Varianz der Residuen (β0={res['beta_0']}, β1={res['beta_1']}): {res['varianz_residuen']:.4f}\")\n",
+    "\n",
+    "plt.tight_layout()\n",
+    "plt.show()"
+   ]
   }
  ],
  "metadata": {