diff --git a/OptimalTransportWasserteinDistance.ipynb b/OptimalTransportWasserteinDistance.ipynb
index 468bceb..5c61bfc 100644
--- a/OptimalTransportWasserteinDistance.ipynb
+++ b/OptimalTransportWasserteinDistance.ipynb
@@ -583,7 +583,7 @@
     "\\begin{align*}\\tag{1.6}\n",
     "    \\sum_{i=0}^{N-1} a_i log\\left(\\frac{a_i}{b_i}\\right) &\\geq \\left(\\sum_{i=0}^{N-1} a_i\\right) log\\left(\\frac{\\sum_{i=0}^{N-1}a_i}{\\sum_{i=0}^{N-1}b_i}\\right)\n",
     "\\end{align*}\n",
-    "Where $a_i,b_i \\in [\\mathbb{R}^{+} \\times \\mathbb{R}^{+}]$, $a=\\sum_{i=0}^{N-1} a_i$, $b=\\sum_{i=0}^{N-1} b_i = 1$.\n",
+    "Where $a_i,b_i \\in [\\mathbb{R}^{+} \\times \\mathbb{R}^{+}]$, $a=\\sum_{i=0}^{N-1} a_i$, $b=\\sum_{i=0}^{N-1} b_i = 1$ and $b_i=\\frac{1}{N}$.\n",
     "\n",
     "ie:\n",
     "\\begin{align*}\n",
diff --git a/SimpleChangeDetection.ipynb b/SimpleChangeDetection.ipynb
new file mode 100644
index 0000000..51ca9cc
--- /dev/null
+++ b/SimpleChangeDetection.ipynb
@@ -0,0 +1,52 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "c4b857d5-ca08-4681-8ac7-f8717909fa68",
+   "metadata": {},
+   "source": [
+    "# Change detection in time serie: a small example"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4a4a9e99-53bb-4d92-b227-e944d93585ab",
+   "metadata": {},
+   "source": [
+    "## Sources/documentation\n",
+    "* Change point detection example with various technics [from forecastegy](https://forecastegy.com/posts/change-point-detection-time-series-python/)\n",
+    "* Cherry-tree blossom date in kyoto dataset: [download here](https://ourworldindata.org/grapher/date-of-the-peak-cherry-tree-blossom-in-kyoto)\n",
+    "* Sample of bayesian reasoning on switch detection: [Notebook sample from the Bayesian Methods for Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/blob/master/Chapter1_Introduction/Ch1_Introduction_PyMC3.ipynb)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8bf8f020-51bb-4b35-a6ce-bcb22de6e4f1",
+   "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": "3.12.1"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}