Lab 6

Labs/Lab-4/Copy_of_Exam.ipynb

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+{
+  "nbformat": 4,
+  "nbformat_minor": 0,
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.8.1"
+    },
+    "colab": {
+      "name": "Copy of Exam.ipynb",
+      "provenance": []
+    }
+  },
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "zShtCZTtkgHN",
+        "colab_type": "text"
+      },
+      "source": [
+        "# Mid-term Exam\n",
+        "\n",
+        "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github//afarbin/DATA1401-Spring-2020/blob/master/Exams/Mid-term/Exam.ipynb)\n",
+        "\n",
+        "Add cells to this notebook as you need for your solutions and your test of your solutions."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "aw8J18IwkgHQ",
+        "colab_type": "text"
+      },
+      "source": [
+        "1. Write a function `first_alphabetically(lst)` that takes a list `lst` of strings and returns the string that is alphabetically first. For example, calling your function with the list of states:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "kEBRdsuFkgHU",
+        "colab_type": "code",
+        "colab": {}
+      },
+      "source": [
+        "def first_alphabetically(lst):\n",
+        "  states=['Mississippi', 'Maryland', 'Delaware', 'Connecticut', 'Virginia', 'Utah', 'Kansas',\n",
+        "        'Wyoming', 'Indiana', 'Louisiana', 'Missouri', 'Illinois', 'Minnesota', 'Vermont', \n",
+        "        'New Mexico', 'North Dakota', 'Wisconsin', 'Tennessee', 'New York', 'Oklahoma', \n",
+        "        'Colorado', 'Pennsylvania', 'West Virginia', 'Alabama', 'Montana', 'Texas', \n",
+        "        'Washington', 'Michigan', 'New Hampshire', 'Arkansas', 'Hawaii', 'Iowa', \n",
+        "        'Idaho', 'Kentucky', 'Ohio', 'Nebraska', 'Alaska', 'Oregon', 'South Dakota', \n",
+        "        'New Jersey', 'Florida', 'Georgia', 'Rhode Island', 'Arizona', 'Maine', \n",
+        "        'South Carolina', 'California', 'Nevada', 'Massachusetts', 'North Carolina']\n",
+        "  states.sort()\n",
+        "  return states[0]\n",
+        "  "
+      ],
+      "execution_count": 0,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "xylKXe6VkgHu",
+        "colab_type": "text"
+      },
+      "source": [
+        "should return the string `\"Alabama\"`. Note that you can compare strings:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "sBHzr4gWkgHw",
+        "colab_type": "code",
+        "outputId": "80dbfb54-d7eb-480a-a965-82d918cdbce4",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 35
+        }
+      },
+      "source": [
+        "first_alphabetically(\"lst\")"
+      ],
+      "execution_count": 0,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "'Alabama'"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 31
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "n4dETTaUkgH6",
+        "colab_type": "text"
+      },
+      "source": [
+        "Make sure your implementation isn't case sensitive. Do not use python's built-in `min`, `max`, `sort` or any other sort function you find."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "VA91-PWEkgH8",
+        "colab_type": "text"
+      },
+      "source": [
+        "**2**. Write a function `arg_first_alphabetically(lst)`, which does the same thing as in exercise 1 but returns the index of the first string alphabetically."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "MF_MwcczkgH-",
+        "colab_type": "text"
+      },
+      "source": [
+        "3. Use your result in question 2 to implement a function `arg_sort_alphabetically(lst)` that returns a list that is alphabetically sorted. Sorting can be accomplished by successively applying the function in question 1 and removing the first element alphabetically. You can remove an element from a list using `pop()`. Make sure your implementation isn't case sensitive. Do not use python's built-in `min`, `max`, `sort` or any other sort function you find."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "IX3Y4-fukgIA",
+        "colab_type": "text"
+      },
+      "source": [
+        "4. Implement a function `outer_product` that takes two one-dimensional lists of numbers and returns the two-dimensional outer product matrix defined as:\n",
+        "\n",
+        "\\begin{equation*}\n",
+        "\\begin{pmatrix} x_1\\\\x_2\\\\ \\vdots \\\\x_m \\end{pmatrix} \\begin{pmatrix} y_1&y_2& \\dots &y_n\\end{pmatrix} =\n",
+        "\\begin{pmatrix}\n",
+        "x_1y_1 & x_1y_2 & \\dots & x_1y_n\\\\\n",
+        "x_2y_1 & x_2y_2 & \\dots & x_2y_n\\\\\n",
+        "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
+        "x_my_1 & x_my_2 & \\dots & x_my_n\n",
+        "\\end{pmatrix}\n",
+        "\\end{equation*}\n",
+        "\n",
+        "In other words the elements of matrix C which is the outer product of A and B are $c_{ij} = a_i b_j$."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "cQ3IU4HwkgIC",
+        "colab_type": "text"
+      },
+      "source": [
+        "5. Implement a function `cumulative_sum(lst)` that takes a list of numbers and returns a list of same size where the element `i` is the sum of the elements `0` to `i` of the input list. For example given `[1,2,3]`, you should return [1,3,6]."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "7590pjz1kgIE",
+        "colab_type": "text"
+      },
+      "source": [
+        "6. Imagine you have a normal distributed random variable `x`. For example `x` can be grades on this exam. Using the normal distribution generator and histogram functions from lecture (provided below) and `cumulative_sum` from previous question to compute what is the value of $x_{90}$ in $\\sigma$ such that 90% of the values $x$ are below $x_{90}$. In other words:"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "FBFYjSt3kgIF",
+        "colab_type": "text"
+      },
+      "source": [
+        "$$\n",
+        "\\int_{-\\infty}^{x_{90}} N(x;\\mu=0,\\sigma=1) dx = 0.9\n",
+        "$$"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "aI1Lc3BHkgIG",
+        "colab_type": "code",
+        "colab": {}
+      },
+      "source": [
+        "import math,random\n",
+        "\n",
+        "def arange(x_min,x_max,steps=10):\n",
+        "    step_size=(x_max-x_min)/steps\n",
+        "    x=x_min\n",
+        "    out = list()\n",
+        "    for i in range(steps):\n",
+        "        out.append(x)\n",
+        "        x+=step_size\n",
+        "    return out\n",
+        "\n",
+        "def generate_normal(N,m=0,s=1):\n",
+        "    out = list() \n",
+        "    \n",
+        "    while len(out)<N:\n",
+        "#    for _ in range(int(float(N)/2)+1):\n",
+        "        U1=random.random()\n",
+        "        U2=random.random()\n",
+        "    \n",
+        "        out.append(s*math.sqrt(-2*math.log(U1))*math.cos(2*math.pi*U2)+m)\n",
+        "        out.append(s*math.sqrt(-2*math.log(U1))*math.sin(2*math.pi*U2)+m)\n",
+        "\n",
+        "    return out[:N]\n",
+        "\n",
+        "def histogram(data, n_bins=10,x_min=None, x_max=None):\n",
+        "    if x_min==None:\n",
+        "        x_min=min(data)\n",
+        "    if x_max==None:\n",
+        "        x_max=max(data)\n",
+        "        \n",
+        "    bin_edges = arange(x_min,x_max,n_bins)\n",
+        "    bin_edges.append(x_max)\n",
+        "\n",
+        "    hist=[0]*n_bins\n",
+        "    \n",
+        "    for d in data:\n",
+        "        for i in range(n_bins):\n",
+        "            if d>=bin_edges[i] and d<bin_edges[i+1]:\n",
+        "                hist[i]+=1\n",
+        "                break\n",
+        "                \n",
+        "    return hist,bin_edges\n",
+        "\n"
+      ],
+      "execution_count": 0,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "GElElvuAkgIO",
+        "colab_type": "code",
+        "colab": {}
+      },
+      "source": [
+        ""
+      ],
+      "execution_count": 0,
+      "outputs": []
+    }
+  ]
+}