r_notebook.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyM7j1bTwdwm36VTLSrQGIU/",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "ir",
      "display_name": "R"
    },
    "language_info": {
      "name": "R"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/ahmedmoustafa/Notebooks/blob/main/r_notebook.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# R Notebook"
      ],
      "metadata": {
        "id": "9L_XiktP2k8x"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "NXnnwBmO1L2v",
        "outputId": "04f96772-257f-4e39-f908-d336e22c3a16"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "2"
            ],
            "text/markdown": "2",
            "text/latex": "2",
            "text/plain": [
              "[1] 2"
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "1 + 1"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x = rnorm(100000, 0, 1)\n",
        "head(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "9lyY_CS-1TJ-",
        "outputId": "f3da3499-26c3-4dcc-971d-64f94d76be3c"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<style>\n",
              ".list-inline {list-style: none; margin:0; padding: 0}\n",
              ".list-inline>li {display: inline-block}\n",
              ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
              "</style>\n",
              "<ol class=list-inline><li>-1.21668075999988</li><li>1.46785704135263</li><li>2.09425418556824</li><li>1.38413749429001</li><li>0.307432762124115</li><li>-0.728360117989135</li></ol>\n"
            ],
            "text/markdown": "1. -1.21668075999988\n2. 1.46785704135263\n3. 2.09425418556824\n4. 1.38413749429001\n5. 0.307432762124115\n6. -0.728360117989135\n\n\n",
            "text/latex": "\\begin{enumerate*}\n\\item -1.21668075999988\n\\item 1.46785704135263\n\\item 2.09425418556824\n\\item 1.38413749429001\n\\item 0.307432762124115\n\\item -0.728360117989135\n\\end{enumerate*}\n",
            "text/plain": [
              "[1] -1.2166808  1.4678570  2.0942542  1.3841375  0.3074328 -0.7283601"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "hist(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "hfZYwqHV1kxZ",
        "outputId": "b7e52fee-2b83-4010-b997-897b45642f05"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Histogram of x”"
            ],
            "image/png": 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LPZRxBSPYQUEOuQPvNg+eMXDkyf3M15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\nACEBAggJEPD/AZiHRhJbzkZCAAAAAElFTkSuQmCC"
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "length(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "JA-3mvUj2EaH",
        "outputId": "61a51f75-b1fb-45e8-c318-9e7e1c4f1742"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "100000"
            ],
            "text/markdown": "100000",
            "text/latex": "100000",
            "text/plain": [
              "[1] 100000"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "mean(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "XLIe2rSA2WXs",
        "outputId": "d1a14a99-e0e9-4c9b-e7e7-b06fa7b6e51e"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "-0.00017738247156153"
            ],
            "text/markdown": "-0.00017738247156153",
            "text/latex": "-0.00017738247156153",
            "text/plain": [
              "[1] -0.0001773825"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "sd(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "8mVDShj52aUE",
        "outputId": "a5cb1632-8dc7-4489-a6ee-f38334b60e88"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "1.00324648172719"
            ],
            "text/markdown": "1.00324648172719",
            "text/latex": "1.00324648172719",
            "text/plain": [
              "[1] 1.003246"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "MlUKPxbA2eIR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "UAw8Wy9P2kJb"
      }
    }
  ]
}