_doc/notebooks/td2a/td2a_correction_session_2A.ipynb

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    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# 2A.data - Calcul Matriciel, Optimisation - correction\n",
        "\n",
        "Calcul matriciel ([numpy](http://www.numpy.org/))."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Populating the interactive namespace from numpy and matplotlib\n"
          ]
        }
      ],
      "source": [
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [
        {
          "data": {
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              "<b>Plan</b>\n",
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              "            // passer \u00e0 child suivant (le chercher)\n",
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              "            // in a notebook\n",
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              "\n",
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              "<IPython.core.display.HTML object>"
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          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "from jyquickhelper import add_notebook_menu\n",
        "add_notebook_menu()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Exercice 1: Echiquier et Crible d'Erathosthene"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "* Exercice 1-A Echiquier: Cr\u00e9er une matrice \u00e9chiquier (des 1 et des 0 altern\u00e9s) de taille 8x8, de deux fa\u00e7ons diff\u00e9rentes\n",
        "    * en vous servant de slices \n",
        "    * en vous servant de la fonction [tile](http://docs.scipy.org/doc/numpy/reference/generated/numpy.tile.html#numpy.tile)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[1 0 1 0 1 0 1 0]\n",
            " [0 1 0 1 0 1 0 1]\n",
            " [1 0 1 0 1 0 1 0]\n",
            " [0 1 0 1 0 1 0 1]\n",
            " [1 0 1 0 1 0 1 0]\n",
            " [0 1 0 1 0 1 0 1]\n",
            " [1 0 1 0 1 0 1 0]\n",
            " [0 1 0 1 0 1 0 1]]\n",
            "[[1 0 1 0 1 0 1 0]\n",
            " [0 1 0 1 0 1 0 1]\n",
            " [1 0 1 0 1 0 1 0]\n",
            " [0 1 0 1 0 1 0 1]\n",
            " [1 0 1 0 1 0 1 0]\n",
            " [0 1 0 1 0 1 0 1]\n",
            " [1 0 1 0 1 0 1 0]\n",
            " [0 1 0 1 0 1 0 1]]\n"
          ]
        }
      ],
      "source": [
        "import numpy as np\n",
        "#Exo1a-1:\n",
        "chess = np.zeros((8,8), dtype=int)\n",
        "chess[::2,::2] = 1\n",
        "chess[1::2,1::2] = 1\n",
        "print(chess)\n",
        "\n",
        "#Exo1a-2:\n",
        "chess2 = np.tile([[1,0],[0,1]], (4,4))\n",
        "print(chess2)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "* Exercice 1-B Pi\u00e8ge lors d'une extraction 2d:\n",
        "    * D\u00e9finir la matrice $M = \\left(\\begin{array}{ccccc} 1 & 5 & 9 & 13 & 17 \\\\ 2 & 6 & 10 & 14 & 18 \\\\ 3 & 7 & 11 & 15 & 19 \\\\ 4 & 8 & 12 & 16 & 20 \\\\ \\end{array}\\right)$\n",
        "    * En **extraire** la matrice $\\left(\\begin{array}{ccc} 6 & 18 & 10 \\\\ 7 & 19 & 11 \\\\ 5 & 17 & 9 \\\\ \\end{array}\\right)$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[ 1  5  9 13 17]\n",
            " [ 2  6 10 14 18]\n",
            " [ 3  7 11 15 19]\n",
            " [ 4  8 12 16 20]]\n",
            "WRONG: [ 6 19  9]\n",
            "########\n",
            "[[ 6 18 10]\n",
            " [ 7 19 11]\n",
            " [ 5 17  9]]\n",
            "(array([[1],\n",
            "       [2],\n",
            "       [0]]), array([[1, 4, 2]]))\n",
            "[[ 6 18 10]\n",
            " [ 7 19 11]\n",
            " [ 5 17  9]]\n"
          ]
        }
      ],
      "source": [
        "#Exo1B:\n",
        "M = np.arange(1, 21).reshape((4,5), order='F')\n",
        "print(M)\n",
        "\n",
        "idx_row = [1, 2, 0]\n",
        "idx_col = [1, 4, 2]\n",
        "#the following line is wrong: it create couples from the two lists\n",
        "print(\"WRONG:\",M[idx_row, idx_col])\n",
        "print(\"########\")\n",
        "# first correct way:\n",
        "print(M[idx_row][:,idx_col])\n",
        "# we can also use broadcasted indices to create all the couples we want: \n",
        "idx = np.ix_(idx_row, idx_col)\n",
        "print(idx)\n",
        "print(M[idx])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "* Exercice 1-C Crible d'Erathosthene: On souhaite impl\u00e9menter un [crible d'Erathosth\u00e8ne](http://fr.wikipedia.org/wiki/Crible_d'%C3%89ratosth%C3%A8ne) pour trouver les nombres premiers inf\u00e9rieurs \u00e0 $N=1000$.\n",
        "    * partir d'un array de bool\u00e9ens de taille N+1, tous \u00e9gaux \u00e0 True.\n",
        "    * Mettre 0 et 1 \u00e0 False car ils ne sont pas premiers\n",
        "    * pour chaque entier $k$ entre 2 et $\\sqrt{N}$: \n",
        "        * si $k$ est premier: on passe ses multiples (entre $k^2$ et $N$) \u00e0 False\n",
        "    * on print la liste des entiers premiers"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[  2   3   5   7  11  13  17  19  23  29  31  37  41  43  47  53  59  61\n",
            "  67  71  73  79  83  89  97 101 103 107 109 113 127 131 137 139 149 151\n",
            " 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251\n",
            " 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359\n",
            " 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463\n",
            " 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593\n",
            " 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701\n",
            " 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827\n",
            " 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953\n",
            " 967 971 977 983 991 997]\n"
          ]
        }
      ],
      "source": [
        "#Exo1c\n",
        "n = 1001\n",
        "is_prime = np.ones(n, dtype=bool)\n",
        "is_prime[:2] = False\n",
        "\n",
        "for k in range(2, int(np.sqrt(n))+1):\n",
        "    is_prime[k**2::k] = False\n",
        "print(np.arange(n)[is_prime])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "On remarque que le nombre 6 est barr\u00e9 deux fois car il est multiple de 3 et de 2. Cela signifie que le nombre 6 est barr\u00e9 durant les deux premi\u00e8res it\u00e9rations. En fait chaque nombre ``k*i`` est n\u00e9cessaire barr\u00e9 dans une pr\u00e9c\u00e9dente it\u00e9ration si ``i<k``. On remplace donc ``k*i`` par ``k*k`` ou ``k**2``."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[  2   3   5   7  11  13  17  19  23  29  31  37  41  43  47  53  59  61\n",
            "  67  71  73  79  83  89  97 101 103 107 109 113 127 131 137 139 149 151\n",
            " 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251\n",
            " 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359\n",
            " 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463\n",
            " 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593\n",
            " 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701\n",
            " 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827\n",
            " 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953\n",
            " 961 967 971 977 983 991 997]\n"
          ]
        }
      ],
      "source": [
        "#Exo1c\n",
        "import numpy as np\n",
        "n = 1001\n",
        "is_prime = np.ones(n, dtype=bool)\n",
        "is_prime[:2] = False\n",
        "for k in range(2, int(np.sqrt(n))):\n",
        "    is_prime[k*k::k] = False\n",
        "print(np.arange(n)[is_prime])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Exercice 2 : marches al\u00e9atoires"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Simulez (**en une seule fois!**) 10000 marches al\u00e9atoires de taille 1000, partant de 0 et de pas +1 ou -1 \u00e9quiprobables \n",
        "\n",
        "* Faites un graphe repr\u00e9sentant la racine de la moyenne des carr\u00e9s des positions (=cumul des pas \u00e0 un instant donn\u00e9) en fonction du temps\n",
        "* Quels sont les amplitudes maximales et minimales atteintes parmi l'ensemble des marches al\u00e9atoires?\n",
        "* Combien de marches s'\u00e9loigne de plus de 50 de l'origine?\n",
        "* Parmi celles qui le font, quelle est la moyenne des temps de passage (i.e. le premier moment o\u00f9 ces marches d\u00e9passent +/-50)?\n",
        "\n",
        "Vous aurez peut-\u00eatre besoin des fonctions suivantes: [np.abs](http://docs.scipy.org/doc/numpy/reference/generated/numpy.absolute.html), [np.mean](http://docs.scipy.org/doc/numpy/reference/generated/numpy.mean.html), [np.max](http://docs.scipy.org/doc/numpy/reference/generated/numpy.maximum.html), [np.where](http://docs.scipy.org/doc/numpy/reference/generated/numpy.where.html), [np.argmax](http://docs.scipy.org/doc/numpy/reference/generated/numpy.argmax.html), [np.any](http://docs.scipy.org/doc/numpy/reference/generated/numpy.any.html), [np.cumsum](http://docs.scipy.org/doc/numpy/reference/generated/numpy.cumsum.html), [np.random.randint](http://docs.scipy.org/doc/numpy/reference/generated/numpy.random.randint.html)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[  1,   2,   3,   4,   5,   6,   5,   4,   5,   4],\n",
              "       [  1,   0,   1,   2,   1,   0,   1,   2,   1,   2],\n",
              "       [ -1,  -2,  -3,  -4,  -5,  -6,  -7,  -8,  -9, -10],\n",
              "       [  1,   0,   1,   2,   3,   2,   3,   4,   5,   6],\n",
              "       [ -1,  -2,  -1,   0,  -1,   0,  -1,   0,  -1,  -2],\n",
              "       [ -1,   0,   1,   2,   3,   4,   3,   4,   3,   2],\n",
              "       [ -1,   0,   1,   0,   1,   2,   3,   4,   5,   4],\n",
              "       [ -1,  -2,  -1,   0,   1,   2,   1,   2,   3,   2],\n",
              "       [  1,   0,  -1,   0,  -1,  -2,  -3,  -4,  -3,  -4],\n",
              "       [  1,   0,  -1,   0,   1,   2,   1,   2,   3,   4]], dtype=int32)"
            ]
          },
          "execution_count": 8,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import numpy as np\n",
        "\n",
        "n_walks = 10000\n",
        "n_steps = 1000\n",
        "steps = np.random.randint(0, 2, (n_walks, n_steps))\n",
        "steps = 2*steps-1 \n",
        "walks = np.cumsum(steps, axis=1)\n",
        "\n",
        "# on affiche le premier carr\u00e9 10x10\n",
        "walks[:10,:10]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Highest position:133\tLowest position:-120\n",
            "Number of walks over bound(=50):2074\n",
            "Mean crossing time:673.8341369334619\n"
          ]
        },
        {
          "data": {
            "image/png": 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gjogrmxqR772qNj6mtwjJ4hFQ+XtVoMKWDB+LNvksVacQaLf/Hn2WO6S21Xbc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23bjM08gWX70Wm5XGh+d3j1pZpPn1K/iBF+kqWBPuzAAgIyAiqOalFJNmnrBYFG6APoZf+72gEd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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x6f2c160>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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zZdkyT5a+fhyPtWt5cc1KPA//ab8/p3lzDrUeQvATfVD+/jfYkyiPpPAL4QTS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\n4RdCCCcjhV8IIZzM/wNEXVBhcjIITAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x95f4358>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "# let's have a quick look at a few random walks\n",
        "plt.plot(walks[:10,:].transpose())\n",
        "plt.title('A few random walks')\n",
        "# Let's see how the root mean square of the position evolves with time/nb of steps\n",
        "rms_position = np.sqrt( (walks**2).mean(axis=0) )\n",
        "plt.figure()\n",
        "t = 1 + np.arange(len(rms_position))\n",
        "plt.plot(t, np.sqrt(t), ':b', lw=3) #Just to show the fit \n",
        "plt.plot(t, rms_position, '-r', lw=2)\n",
        "plt.title('Root Mean Square of Position by Time')\n",
        "# What are the highest/lowest positions \n",
        "print('Highest position:{max}\\tLowest position:{min}'.format(max=walks.max(), min=walks.min()))\n",
        "# How many walks wander further than 50?\n",
        "bound = 50\n",
        "hits_the_bound = np.any(np.abs(walks)> bound, axis=1) #for each walk, do we go further than the bound at any time?\n",
        "print('Number of walks over bound(={}):{}'.format(bound, hits_the_bound.sum()))\n",
        "# Among the walks that go beyond the bound, what is the mean of the first hits?\n",
        "# we use argmax on the boolean array to get the first True value\n",
        "first_hits = (np.abs(walks[hits_the_bound,:])>bound).argmax(axis=1)\n",
        "print('Mean crossing time:{}'.format(first_hits.mean()))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Exercice 3 : retrouver la s\u00e9rie al\u00e9atoire \u00e0 partir des marches al\u00e9atoires\n",
        "\n",
        "Dans cet exercice, on cherche \u00e0 retrouver la s\u00e9rie initiale \u00e0 partir de la somme cumul\u00e9e de celle-ci. On veut calculer en quelque sort sa d\u00e9riv\u00e9e."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 1,  1,  1,  1,  1, -1, -1,  1, -1,  1],\n",
              "       [-1,  1,  1, -1, -1,  1,  1, -1,  1, -1],\n",
              "       [-1, -1, -1, -1, -1, -1, -1, -1, -1, -1],\n",
              "       [-1,  1,  1,  1, -1,  1,  1,  1,  1,  1],\n",
              "       [-1,  1,  1, -1,  1, -1,  1, -1, -1, -1],\n",
              "       [ 1,  1,  1,  1,  1, -1,  1, -1, -1,  1],\n",
              "       [ 1,  1, -1,  1,  1,  1,  1,  1, -1,  1],\n",
              "       [-1,  1,  1,  1,  1, -1,  1,  1, -1, -1],\n",
              "       [-1, -1,  1, -1, -1, -1, -1,  1, -1,  1],\n",
              "       [-1, -1,  1,  1,  1, -1,  1,  1,  1,  1]], dtype=int32)"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "derivee = walks[:,1:] - walks[:,:-1]\n",
        "derivee[:10,:10]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Exercice 4 : simulation, r\u00e9gression, estimation par maximisation de la vraisemblance"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "* On commence par simuler la variable $Y = 3 X_1 -2 X_2 +2 + \\epsilon$ o\u00f9 $X_1,X_2,\\epsilon \\sim \\mathcal{N}(0,1)$ \n",
        "* On souhaite ensuite retrouver les coefficients dans la [r\u00e9gression lin\u00e9aire](http://fr.wikipedia.org/wiki/R%C3%A9gression_lin%C3%A9aire) de $Y$ sur $X_1$ et $X_2$ dans un mod\u00e8le avec constante, par la m\u00e9thode des Moindres Carr\u00e9s Ordinaires. On rappelle que la forme matricielle de l'estimateur des MCO est $\\hat{\\beta} = (X'X)^{-1}X'Y$\n",
        "* Enfin, $Y$ \u00e9tant normale, on souhaite estimer ses param\u00e8tres par maximisation de vraisemblance:\n",
        "    * La densit\u00e9 s'\u00e9crit: $f(x, \\mu, \\sigma) = \\frac{1}{\\sigma \\sqrt{2\\pi} } e^{ -\\frac{(x-\\mu)^2}{2\\sigma^2} }$\n",
        "    * La log-vraisemblance: $\\ln\\mathcal{L}(\\mu,\\sigma^2) = \\sum_{i=1}^n \\ln f(x_i;\\,\\mu,\\sigma^2) = -\\frac{n}{2}\\ln(2\\pi) - \\frac{n}{2}\\ln\\sigma^2 - \\frac{1}{2\\sigma^2}\\sum_{i=1}^n (x_i-\\mu)^2$ ou encore en divisant par $n$ : $-\\frac{1}{2}\\ln(2\\pi) - \\frac{1}{2}\\ln\\sigma^2 - \\frac{1}{2n\\sigma^2}\\sum_{i=1}^n (x_i-\\mu)^2$\n",
        "    * L'\u00e9criture des conditions au premier ordre donne une formule ferm\u00e9e pour les estimateurs du maximum de vraisemblance: $\\hat{\\mu} = \\overline{x} \\equiv \\frac{1}{n}\\sum_{i=1}^n x_i$, $\\hat{\\sigma}^2 = \\frac{1}{n} \\sum_{i=1}^n (x_i - \\overline{x})^2$.\n",
        "    * V\u00e9rifiez en les impl\u00e9mentant directement que vous trouvez bien la m\u00eame solution que le minimum obtenu en utilisant *scipy.optimize.minimize* pour minimiser l'oppos\u00e9 de la log-vraissemblance.\n",
        "    \n",
        "**version matricielle**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "coef X1, coef X2, constante\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "array([ 2.99395809, -2.00169881,  2.00215411])"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import numpy as np\n",
        "import math\n",
        "from scipy.optimize import minimize\n",
        "n_samples = 100000\n",
        "x1_x2_eps = np.random.randn(n_samples,3)\n",
        "y = 3*x1_x2_eps[:,0] - 2*x1_x2_eps[:,1] + 2 + x1_x2_eps[:,2]\n",
        "\n",
        "X = np.hstack( (x1_x2_eps[:,:2], np.ones((n_samples,1))) )\n",
        "beta_hat = ( np.linalg.inv((X.T).dot(X)) ).dot( (X.T).dot(y) )\n",
        "print(\"coef X1, coef X2, constante\")\n",
        "beta_hat"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**version scipy**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "  status: 0\n",
              " message: 'Optimization terminated successfully.'\n",
              " success: True\n",
              "     nit: 30\n",
              "     fun: 1.8165031271016212\n",
              "    nfev: 57\n",
              "       x: array([  1.99871699,  13.91551151])"
            ]
          },
          "execution_count": 12,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "def log_likelihood(mu,sigma_square, x):\n",
        "    return - 0.5 * math.log(sigma_square) - sum((x - mu)**2)/(2*sigma_square) / len(x)\n",
        "\n",
        "def neg_log_likelihood_vectorielle(theta):\n",
        "    return -log_likelihood(theta[0],theta[1],y)\n",
        "\n",
        "theta0 = np.array([2., 14])\n",
        "optim_res = minimize(neg_log_likelihood_vectorielle, theta0, method='Nelder-Mead')\n",
        "optim_res"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Est-ce bien le r\u00e9sultat attendu :\n",
        "\n",
        "* $\\mathbb{E}Y = 3\\mathbb{E}X_1 - 2\\mathbb{E}X_2 + 2 + \\mathbb{E}\\epsilon = 2$\n",
        "* $\\mathbb{V}Y = 9\\mathbb{V}X_1 + 4\\mathbb{V}X_2 + \\mathbb{V}\\epsilon = 14$\n",
        "\n",
        "Toutes les variables sont ind\u00e9pendantes. On v\u00e9rifie que cela correspond aux r\u00e9ponses cherch\u00e9es :"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(1.9987233148817718, 13.91554073655678)"
            ]
          },
          "execution_count": 13,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "np.mean(y), np.std(y)**2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Exercice 5 :  Optimisation quadratique (sous contraintes) avec cvxopt\n",
        "\n",
        "voir [correction](http://www.xavierdupre.fr/app/ensae_teaching_cs/helpsphinx/notebooks/td1a_correction_session9.html#td1acorrectionsession9rst)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "collapsed": true
      },
      "outputs": [],
      "source": []
    }
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