Tutorial3_SciPy.ipynb

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      "source": [
        "# Probability and Statistics Fall 1400\n",
        "## Python Tutorial - Part3_SciPy\n",
        "\n",
        "* Prepared by : Shayan Vassef\n",
        "* Email : sh.vassef@ut.ac.ir\n",
        "\n",
        "![Python](https://drive.google.com/uc?export=view&id=1Rhyh-TU_iUGeCvIHDrOjFZDLdMgAP5DZ)"
      ]
    },
    {
      "cell_type": "markdown",
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      "source": [
        "# Let's get started !"
      ]
    },
    {
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      "source": [
        "\n",
        "**This notebook will just go through the following topics in order:**\n",
        "\n",
        "* SciPy\n",
        "    * Binomial Distribution\n",
        "      * cdf\n",
        "      * pmf\n",
        "      * sf\n",
        "      * mean\n",
        "      * var\n",
        "      * std \n",
        "    * Poisson Distribution\n",
        "      * cdf\n",
        "      * pmf\n",
        "      * sf\n",
        "      * mean\n",
        "      * var\n",
        "      * std \n",
        "    * Normal Distribution\n",
        "      * cdf\n",
        "      * pdf\n",
        "      * sf\n",
        "      * mean\n",
        "      * var\n",
        "      * std \n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "7d8f509a",
      "metadata": {
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      },
      "source": [
        "# Introducing scipy\n",
        "This module contains a large number of probability distributions as well as a growing library of statistical functions."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "7378f062",
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      "source": [
        "* Python SciPy has modules for the following tasks:\n",
        "  * Optimization\n",
        "  * Linear algebra\n",
        "  * Integration\n",
        "  * Interpolation\n",
        "  * Special functions\n",
        "  * FFT\n",
        "  * Signal and Image processing\n",
        "  * ODE solvers"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "6cb02f11",
      "metadata": {
        "id": "6cb02f11"
      },
      "source": [
        "## How to Install SciPy?"
      ]
    },
    {
      "cell_type": "markdown",
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      "metadata": {
        "id": "d28ff8fb"
      },
      "source": [
        "You can use pip to install SciPy-\n",
        "\n",
        "<font color='red'>pip install scipy</font>\n",
        "\n",
        "You can also use conda for the same-\n",
        "\n",
        "<font color='red'>conda install –c anaconda scipy</font>\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "30f99a0b",
      "metadata": {
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      },
      "source": [
        "## SciPy Importing"
      ]
    },
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      "cell_type": "code",
      "execution_count": 1,
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      "source": [
        "import scipy"
      ]
    },
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      "cell_type": "markdown",
      "source": [
        "## You will also want to interact with numpy here. Let’s import that too."
      ],
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      "source": [
        "import numpy as np"
      ],
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      "source": [
        "### <font color='green'>Binomial Distribution</font>"
      ]
    },
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      "source": [
        "from scipy.stats import binom "
      ],
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      "execution_count": 3,
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    {
      "cell_type": "markdown",
      "source": [
        "### Cumulative distribution function - for less than or equal to 3"
      ],
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              "0.7635913575531722"
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      "source": [
        "binom.cdf(3, 25, 0.1)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Probability mass function - for exact three defects"
      ],
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      "id": "ph3vqu0lOSRU"
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          "data": {
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              "0.22649730750222946"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "binom.pmf(3, 25, 0.1)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### for more than 3 (similar to 1-cdf)"
      ],
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      "source": [
        "binom.sf(3, 25, 0.1)"
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              "0.23640864244682805"
            ]
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          "execution_count": 6
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      "source": [
        "### for mean of the distribution"
      ],
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      "source": [
        "binom.mean(25,0.1)"
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            "text/plain": [
              "2.5"
            ]
          },
          "metadata": {},
          "execution_count": 11
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    },
    {
      "cell_type": "markdown",
      "source": [
        "### for variance of the distribution"
      ],
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      "cell_type": "code",
      "source": [
        "binom.var(25,0.1)"
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      "execution_count": 10,
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          "data": {
            "text/plain": [
              "2.25"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
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      "cell_type": "markdown",
      "source": [
        "### for standard deviation of the distribution"
      ],
      "metadata": {
        "id": "KsiMMAraOsnd"
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      "cell_type": "code",
      "source": [
        "binom.std(25,0.1)"
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              "1.5"
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          "metadata": {},
          "execution_count": 9
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    {
      "cell_type": "markdown",
      "source": [
        "### <font color='green'>Poisson Distribution</font>"
      ],
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    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import poisson  "
      ],
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      },
      "id": "DzMsEwALPXDA",
      "execution_count": 12,
      "outputs": []
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    {
      "cell_type": "code",
      "source": [
        "poisson.pmf(7, 5) "
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      "execution_count": 14,
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              "0.10444486295705395"
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          },
          "metadata": {},
          "execution_count": 14
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    },
    {
      "cell_type": "markdown",
      "source": [
        "### The same method is applied here (cdf,pmf,sf,mean,var,std)"
      ],
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    {
      "cell_type": "markdown",
      "source": [
        "### <font color='green'>Normal Distribution</font>"
      ],
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    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import norm"
      ],
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        "id": "yGzoEAjuQP6r"
      },
      "id": "yGzoEAjuQP6r",
      "execution_count": 15,
      "outputs": []
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    {
      "cell_type": "code",
      "source": [
        "norm.sf(50, 53, 2)"
      ],
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        },
        "id": "_MikzQs9PlJj",
        "outputId": "c3e0f51b-5fa4-4018-c4e7-1e69f7b6b228"
      },
      "id": "_MikzQs9PlJj",
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9331927987311419"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###  Probability density function (not Probability mass function) - for exact value"
      ],
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        "id": "ibNtwuc6QZl8"
      },
      "id": "ibNtwuc6QZl8"
    },
    {
      "cell_type": "code",
      "source": [
        "x_ax = np.linspace(45,55, 13)\n",
        "x_ax"
      ],
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        },
        "id": "3sJsu-OjQahY",
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      "id": "3sJsu-OjQahY",
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([45.        , 45.83333333, 46.66666667, 47.5       , 48.33333333,\n",
              "       49.16666667, 50.        , 50.83333333, 51.66666667, 52.5       ,\n",
              "       53.33333333, 54.16666667, 55.        ])"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
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        "y_ax = norm.pdf(x_ax, 50, 2)\n",
        "y_ax"
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      "id": "PTnF5ZTtQftL",
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.00876415, 0.02277198, 0.04973857, 0.09132454, 0.14095594,\n",
              "       0.18288618, 0.19947114, 0.18288618, 0.14095594, 0.09132454,\n",
              "       0.04973857, 0.02277198, 0.00876415])"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Thats the END ! :(...\n",
        "# Hope you have learned some new skills during the Tutorials .\n",
        "# Feel Free to share your opinions,feedbacks,... \n"
      ],
      "metadata": {
        "id": "-7Eych69Rh1V"
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      "id": "-7Eych69Rh1V"
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        ""
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      "execution_count": null,
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