{
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  {
   "cell_type": "markdown",
   "id": "146f64d2",
   "metadata": {},
   "source": [
    "# Teorema central do Limite\n",
    "\n",
    "Estatística I - Aeronáutica - 2023/02\n",
    "\n",
    "Thomas Peron \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "fc80451e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Widget Javascript not detected.  It may not be installed or enabled properly.\n"
     ]
    },
    {
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       "model_id": "5cffe6bfb5ab4ccdbb33e6a39e31ec23"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import ipywidgets as widgets\n",
    "from ipywidgets import interactive, Layout\n",
    "\n",
    "from matplotlib import rcParams\n",
    "\n",
    "import matplotlib as mpl \n",
    "mpl.rcParams['figure.dpi'] = 400 \n",
    "mpl.rcParams['figure.figsize'] = (20,3)\n",
    "\n",
    "\n",
    "rcParams['font.family'] = 'serif'\n",
    "rcParams['font.serif'] = 'Times'\n",
    "#rcParams['svg.fonttype'] = 'none'\n",
    "plt.rc('text',usetex=True)\n",
    "\n",
    "\n",
    "def plot_clt(sample_size, num_samples, distribution):\n",
    "    plt.figure(figsize=(10, 6))\n",
    "    sample_means = []\n",
    "\n",
    "    for _ in range(num_samples):\n",
    "        if distribution == 'Uniforme':\n",
    "            data = np.random.uniform(0, 1, sample_size)\n",
    "        elif distribution == 'Exponencial':\n",
    "            data = np.random.exponential(1, sample_size)    \n",
    "        else:\n",
    "            data = np.random.normal(0, 1, sample_size)\n",
    "\n",
    "        sample_means.append(np.mean(data))\n",
    "\n",
    "        \n",
    "    #plt.figure(figsize=(10,6))    \n",
    "    plt.hist(sample_means, bins=50, density=True, alpha=0.6, color='gray',edgecolor='black')\n",
    "    plt.title(r'Visualizando o Teorema Central do Limite',fontsize=16)\n",
    "    plt.xlabel(r'Média empírica, $\\bar{X}_n$',fontsize=16)\n",
    "    plt.ylabel(r'Frequência',fontsize=16)\n",
    "    plt.show()\n",
    "\n",
    "# Create interactive widget\n",
    "widget = interactive(\n",
    "    plot_clt,\n",
    "    sample_size=widgets.IntSlider(min=1, max=3000, step=10, value=10, description=r'Tamanho da amostra, $\\bar{X}_n = \\frac{1}{n}(X_1 + X_2 + \\cdots + X_n)$:'),\n",
    "    num_samples=widgets.IntSlider(min=1, max=3000, step=10, value=100, description='Número de amostras:'),\n",
    "    distribution=widgets.Dropdown(options=['Uniforme', 'Exponencial', 'Normal'], description='Distribuição:')\n",
    ")\n",
    "\n",
    "# Set widget layout\n",
    "widget.layout = Layout(display='flex', flex_flow='column', align_items='center', width='95%')\n",
    "\n",
    "widget\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "904e4d95",
   "metadata": {},
   "outputs": [],
   "source": []
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  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2ab362ee",
   "metadata": {},
   "outputs": [],
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  }
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