diff --git a/exercises/notes.ipynb b/exercises/notes.ipynb
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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "a374c69f",
+   "metadata": {},
+   "source": [
+    "# Lecture 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "76d92d18-1d77-40d2-a910-592183635d3b",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    },
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "mean [1.56535948 1.26470588]\n"
+     ]
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "data = np.loadtxt('./09_data.txt')\n",
+    "\n",
+    "data[0:9]\n",
+    "print(\"mean\", np.mean(data, axis=0))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "5f0f34b4-5bbe-439b-8b4e-fbb05794b790",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    },
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "variance [1.85357128 1.27306805]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"variance\", np.var(data, axis=0))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "70a1920f-beda-4154-ad77-22a9ffe2e39f",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    },
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "standard deviation: [1.36145925 1.12830317]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"standard deviation:\", np.std(data, axis=0))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b70576a2",
+   "metadata": {},
+   "source": [
+    "### Covariance"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "8643c0a4",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 1.85964856 -0.1927676 ]\n",
+      " [-0.1927676   1.27724204]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(np.cov(data, rowvar=False))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "83699a61",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 1.         -0.12507831]\n",
+      " [-0.12507831  1.        ]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(np.corrcoef(data, rowvar=False))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "844b9baa",
+   "metadata": {},
+   "source": [
+    "###  Error propagation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "e7bd0366",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "3.136890603235832\n",
+      "[[2.75135541]]\n",
+      "2.7423640480157205\n",
+      "3.510914605493613\n"
+     ]
+    }
+   ],
+   "source": [
+    "A = np.array([[1, 1]])\n",
+    "V = np.cov(data, rowvar=False)\n",
+    "\n",
+    "print(V[0,0] + V[1,1])\n",
+    "\n",
+    "U = A@V@A.T\n",
+    "\n",
+    "\n",
+    "\n",
+    "print(U)\n",
+    "\n",
+    "print(np.var(data[:,0] + data[:,1]))\n",
+    "\n",
+    "\n",
+    "print(np.var(data[:,0] - data[:,1]))\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7fe1a83d",
+   "metadata": {},
+   "source": [
+    "### Transformation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "545cd923",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.22733602246716966\n",
+      "[0.31675834 0.79736546 0.67625467 ... 0.7802251  0.2300369  0.88856197]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "''"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "rng = np.random.default_rng(12345)\n",
+    "\n",
+    "rfloat = rng.random()\n",
+    "print(rfloat)\n",
+    "u = rng.random(100000)\n",
+    "print(u)\n",
+    "plt.hist(u,bins=100, histtype='step')\n",
+    "plt.hist(np.sqrt(u), bins=100, histtype='step')\n",
+    ";"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "03c8dd26",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.20"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/lecture_1.ipynb b/lecture_1.ipynb
index 04fd9924c902c333e66e429e694e6c51ee44aeb8..9fd5ba18a1d4def2a0eeb0b2488589a7d2e130c8 100644
--- a/lecture_1.ipynb
+++ b/lecture_1.ipynb
@@ -29,6 +29,31 @@
     "hartmut.stadie@uni-hamburg.de"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "754b7855",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "source": [
+    "### Bibliography\n",
+    "\n",
+    "<br>\n",
+    "\n",
+    "\n",
+    "*   Glen Cowan, Statistical Data Analysis,\n",
+    "[pdf](https://www.sherrytowers.com/cowan_statistical_data_analysis.pdf)\n",
+    "<br>\n",
+    "\n",
+    "*  Roger John Barlow, Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences, [lecture notes](https://arxiv.org/pdf/1905.12362.pdf)\n",
+    "<br>\n",
+    "\n",
+    "*   Volker Blobel, Erich Lohrmann, Statistische und numerische Methoden der Datenanalyse,[pdf](https://www.desy.de/~sschmitt/blobel/eBuch.pdf)\n",
+    "        "
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "a3347273",
@@ -1166,51 +1191,6 @@
    "outputs": [],
    "source": []
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "76d92d18-1d77-40d2-a910-592183635d3b",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "print(\"mean\", np.mean(data, axis=0))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "5f0f34b4-5bbe-439b-8b4e-fbb05794b790",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "print(\"variance\", np.var(data, axis=0))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "70a1920f-beda-4154-ad77-22a9ffe2e39f",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "print(\"standard deviation:\", np.std(data, axis=0))"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "20d86d18",
@@ -1220,7 +1200,10 @@
     }
    },
    "source": [
-    "### Exercise: compute covariance and correlation column 1 and 2"
+    "### Exercise: compute covariance and correlation column 1 and 2\n",
+    "\n",
+    "\n",
+    "use `np.cov` and `np.corrcoef`"
    ]
   },
   {
@@ -1242,34 +1225,6 @@
    "outputs": [],
    "source": []
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "751f9384",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "outputs": [],
-   "source": [
-    "print(np.cov(data, rowvar=False))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "abda1c9f",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "outputs": [],
-   "source": [
-    "print(np.corrcoef(data, rowvar=False))"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "eed39982",
@@ -1309,37 +1264,13 @@
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "f88ff1a1",
+   "cell_type": "markdown",
+   "id": "f826b603",
    "metadata": {
     "slideshow": {
-     "slide_type": "skip"
+     "slide_type": "slide"
     }
    },
-   "outputs": [],
-   "source": [
-    "A = np.array([[1, 1]])\n",
-    "V = np.cov(data, rowvar=False)\n",
-    "\n",
-    "print(V[0,0] + V[1,1])\n",
-    "\n",
-    "U = A@V@A.T\n",
-    "\n",
-    "\n",
-    "\n",
-    "print(U)\n",
-    "\n",
-    "print(np.var(data[:,0] + data[:,1]))\n",
-    "\n",
-    "\n",
-    "print(np.var(data[:,0] - data[:,1]))\n"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "f826b603",
-   "metadata": {},
    "source": [
     "### Exercise: Check \"functions of random variables\""
    ]
@@ -1369,39 +1300,6 @@
     " * use [`scipy.stats.norm`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.uniform.html) class\n"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "b424b5b0",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "\n",
-    "rng = np.random.default_rng(12345)\n",
-    "\n",
-    "rfloat = rng.random()\n",
-    "print(rfloat)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "785734fb",
-   "metadata": {
-    "slideshow": {
-     "slide_type": "notes"
-    }
-   },
-   "outputs": [],
-   "source": [
-    "u = rng.random(100000)\n",
-    "print(u)\n",
-    "plt.hist(u,bins=100, histtype='step')\n",
-    "plt.hist(np.sqrt(u), bins=100, histtype='step')\n",
-    ";"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": null,