felipe-gomes-miyazato/tefe-2020-atividade-7.ipynb

## tefe-2020-atividade-7.ipynb
{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "TEFE 2020 - Atividade 7.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyNetcjAVRqRdmTRCdb6gYDi",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/felipe-gm/6e11679da762fa3fb0d4c8a6b8c6474d/tefe-2020-atividade-7.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "89N5swJ_wEoG",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "N = 10000"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hg1DQB6So_p1",
        "colab_type": "text"
      },
      "source": [
        "# Considere a função densidade de probabilidade $f(x) = \\frac{3}{4}(1-x^2)$ para $|x|≤1$. Escreva uma função para gerar $N=10^4$ dados que sigam essa função densidade de probabilidade e responda os itens abaixo:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Hl8gwfGpwK00",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# NxN candidatos a amostras\n",
        "x_s = np.random.default_rng().uniform(-1, 1, (N,N))\n",
        "f_s = np.random.default_rng().uniform(0, 3/4, (N,N))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0oeDo2DtwoL9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "7a37bb6f-3ba6-47e6-f876-fb8d2a318cd0"
      },
      "source": [
        "def f(x): return 3*(1-x**2)/4\n",
        "filtro_exclusao = f_s <= f(x_s)\n",
        "x_raw = x_s[filtro_exclusao]\n",
        "np.shape(x_raw)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(66667865,)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hU7MtQHkZH2A",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "n_sym = len(x_raw)//N # Número de simulações completas com N amostras\n",
        "\n",
        "# Separando simulações completas\n",
        "x_raw = x_raw[:n_sym*N]\n",
        "x = x_raw.reshape((n_sym,N))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "76ug-5MlUsFX",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "ff810715-0807-4193-b920-ffed24ac5bb4"
      },
      "source": [
        "np.shape(x)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(6666, 10000)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "E_hrjobXxxCl",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "outputId": "126e2f02-9356-4599-cc75-e2085fb8dec3"
      },
      "source": [
        "plt.hist(x[:4].T)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([[ 268.,  769., 1102., 1351., 1516., 1465., 1326., 1085.,  791.,\n",
              "          327.],\n",
              "        [ 292.,  772., 1105., 1373., 1469., 1465., 1313., 1079.,  809.,\n",
              "          323.],\n",
              "        [ 303.,  752., 1151., 1336., 1480., 1483., 1371., 1081.,  771.,\n",
              "          272.],\n",
              "        [ 287.,  744., 1018., 1394., 1490., 1520., 1374., 1150.,  761.,\n",
              "          262.]]),\n",
              " array([-9.93733724e-01, -7.95056433e-01, -5.96379143e-01, -3.97701852e-01,\n",
              "        -1.99024561e-01, -3.47270334e-04,  1.98330020e-01,  3.97007311e-01,\n",
              "         5.95684602e-01,  7.94361893e-01,  9.93039184e-01]),\n",
              " <a list of 4 Lists of Patches objects>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T0HQuFH7pkfF",
        "colab_type": "text"
      },
      "source": [
        "### $x_m$\n",
        "\n",
        "$x_m$ é o valor médio de $x$ obtido nas $N$ simulações. A incerteza é pedida no próximo item."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M8kexcWE4-z3",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "094901b5-dc88-4a72-bc60-a9a6666a22d8"
      },
      "source": [
        "x[0].mean()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.0056259044639995195"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "viAybTezaop_",
        "colab_type": "text"
      },
      "source": [
        "### $\\sigma_{x_m}$\n",
        "\n",
        "$\\sigma_{x_m}$ é a incerteza do valor médio de $x$ obtido nas $N$ simulações."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PYGvZ8wouswO",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "bd576d32-cbd0-421c-fd1a-e8b67bad5e08"
      },
      "source": [
        "x_m = x.mean(axis=1)\n",
        "np.shape(x_m)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(6666,)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dzH2J6lNSCnm",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "3587d0a3-32f0-4c72-a23a-092f398f167e"
      },
      "source": [
        "x_m.std(ddof=1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.004502731793864511"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DJFKe75ri-bR",
        "colab_type": "text"
      },
      "source": [
        "## $\\sigma_x$\n",
        "\n",
        "$\\sigma_x$ é o desvio-padrão amostral dos $N$ valores simulados de $x$. Escrever o valor calculado com 5 casas decimais."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yv1HfCoOiz8g",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "bd3f0ef1-c9f0-420a-fb36-4d627ee3acad"
      },
      "source": [
        "sigma_x = x[0].std(ddof=1)\n",
        "sigma_x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.44832108110338353"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dENetzxcke4v",
        "colab_type": "text"
      },
      "source": [
        "## $F_1$\n",
        "\n",
        "$F1$ é a frequência relativa com que foram obtidos valores de $x$ no intervalo entre $x_m - \\sigma_x$ e $x_m + \\sigma_x$. Escrever o valor calculado com 5 casas decimais."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xEtZ63JBkT3G",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "71adcab5-c79e-4c7e-a48c-c100469796b0"
      },
      "source": [
        "np.sum(np.abs(x[0])<sigma_x)/N"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.6245"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jcXhuqxTnYv7",
        "colab_type": "text"
      },
      "source": [
        "# Considere a função densidade de probabilidade $h(y) = \\frac{1}{2} cos(y)$ para $|y|≤\\frac{\\pi}{2}$. Escreva uma função para gerar $N=10^4$ dados que sigam essa função densidade de probabilidade e responda os itens abaixo:\n",
        "\n",
        "A cumulativa é:\n",
        "\n",
        "$$\n",
        "g(y) = \\frac{sin(y) + 1}{2}\n",
        "$$\n",
        "\n",
        "Suponha $g$:  $Uniforme \\left( 0, 1 \\right)$, então\n",
        "\n",
        "$$\n",
        "y = sin^{-1}(2g-1)\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "F7zr6BhAlyuW",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "g = np.random.default_rng().uniform(0, 1, (N,N))\n",
        "\n",
        "y = np.arcsin(2*g - 1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FtJ0uMWBqNzA",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "267c915d-ae04-4d76-9bfe-f5194ee524fe"
      },
      "source": [
        "np.shape(y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10000, 10000)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V1_-vE1pq2tD",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "outputId": "036c9657-d829-49d1-d69a-2dca6fa7f2cc"
      },
      "source": [
        "plt.hist(y[:4].T)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([[ 240.,  635., 1157., 1434., 1522., 1527., 1378., 1113.,  705.,\n",
              "          289.],\n",
              "        [ 250.,  725., 1092., 1355., 1484., 1549., 1442., 1111.,  701.,\n",
              "          291.],\n",
              "        [ 267.,  724., 1058., 1343., 1487., 1574., 1384., 1156.,  766.,\n",
              "          241.],\n",
              "        [ 257.,  645., 1134., 1395., 1526., 1531., 1394., 1130.,  752.,\n",
              "          236.]]),\n",
              " array([-1.56746302, -1.25467792, -0.94189282, -0.62910772, -0.31632262,\n",
              "        -0.00353752,  0.30924758,  0.62203268,  0.93481778,  1.24760288,\n",
              "         1.56038798]),\n",
              " <a list of 4 Lists of Patches objects>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GDJinRTKrTj7",
        "colab_type": "text"
      },
      "source": [
        "### $y_m$\n",
        "\n",
        "$y_m$ é o valor médio de $y$ obtido nas $N$ simulações. A incerteza é pedida no próximo item."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mvWWJp93q5Yw",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "305078b5-3d57-4e71-dc0c-c6e204a882a0"
      },
      "source": [
        "y[0].mean()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.004542148668196087"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oHxtysHJrmY4",
        "colab_type": "text"
      },
      "source": [
        "### $\\sigma_{y_m}$\n",
        "\n",
        "$\\sigma_{y_m}$ é a incerteza do valor médio de y obtido nas N simulações."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "W8JGRCgFrkSF",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "d3206419-4400-4066-c60e-b421d0492855"
      },
      "source": [
        "y_m = y.mean(axis=1)\n",
        "np.shape(y_m)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(10000,)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "W4Tr3p8EvMpH",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "9bde1d18-a884-4fec-a817-5aaf55ce75c6"
      },
      "source": [
        "y_m.std(ddof=1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.006839221227444658"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HvcUfUYmviiv",
        "colab_type": "text"
      },
      "source": [
        "## $\\sigma_y$\n",
        "\n",
        "$\\sigma_y$ é o desvio-padrão amostral dos $N$ valores simulados de $y$. Escrever o valor calculado com 5 casas decimais."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_yJ9Rk0ovROX",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "905a3dfe-0397-44d5-c7bf-064d56fba423"
      },
      "source": [
        "sigma_y = y[0].std(ddof=1)\n",
        "sigma_y"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.6836192068890775"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sOTkjIb5YUDF",
        "colab_type": "text"
      },
      "source": [
        "## $F_1$\n",
        "\n",
        "$F_1$ é a frequência relativa com que foram obtidos valores de $y$ no intervalo entre $y_m-\\sigma_y$ e $y_m+\\sigma_y$. Escrever o valor calculado com 5 casas decimais."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HnI5hy5wwTc2",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "919fe10c-1fd9-4af8-9f09-735947f4edfc"
      },
      "source": [
        "np.sum(np.abs(y[0])<sigma_y)/N"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.631"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    }
  ]
}