finished, try 1

module2/exo1/toy_notebook_en.ipynb

@@ -43,16 +43,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "2.0"
+       "3.128911138923655"
       ]
      },
-     "execution_count": 2,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -63,7 +63,7 @@
     "N = 10000\n",
     "x = np.random.uniform(size=N, low=0, high=1)\n",
     "theta = np.random.uniform(size=N, low=0, high=pi/2)\n",
-    "2/(sum(x+np.sin(theta))>1/N)"
+    "2/(sum((x+np.sin(theta))>1)/N)"
    ]
   },
   {
@@ -109,6 +109,33 @@
     "ax.set_aspect('equal')"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "It is then straightforward to obtain a (not really good) approximation to $\\pi$ by counting how many times, on average, $X^2+Y^2$ is smaller than 1:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "3.112"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "4*np.mean(accept)"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,