sq_01_python_intro/jupyter_book/07_zufallszahlen.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "id": "471b22f4-5b9d-423d-bf7d-6cef078b175e",
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   "source": [
    "# Simulationen\n",
    "\n",
    "Aufbauend auf der letzten Aufgabe möchten wir jetzt simulieren, welches Ertrag wir erwarten können, wenn der Zinnsatz zufällig schwankt. Dafür benötigen wir eine Möglichkeit, diesen Zufall zu berechnen."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b298aa38-556e-43d4-aee1-0047477a53fa",
   "metadata": {},
   "source": [
    "## Zufallszahlen\n",
    "\n",
    "Das Package `random` enthält Funktionen zu Erzeugung von Zufallszahlen.\n",
    "Probieren wir es aus:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2f9a1ee9-0a3f-4ee0-a6e1-d6bc61291889",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "327159f5-1e19-4334-9738-e9cc8a0c9d47",
   "metadata": {},
   "source": [
    "`help(random)` liefert eine lange Dokumentation. Wir brauchen nur einen kleinen Teil davon."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7ba2a1a0-745d-4c9b-bbdf-8e562a445204",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.27\n",
      "0.57\n",
      "0.12\n",
      "3.79\n",
      "1.4\n",
      "1.25\n",
      "1.14\n",
      "0.71\n",
      "3.77\n",
      "0.52\n"
     ]
    }
   ],
   "source": [
    "# Initialisierung - gleicher seed liefert gleiche Zufallszahlen!\n",
    "random.seed(42)\n",
    "samples = 10\n",
    "for i in range(samples):\n",
    "    tmp = random.randint(0, 400)\n",
    "    print(tmp / 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8a2a8fe-fbb4-4ab7-b927-841d949f3cf6",
   "metadata": {},
   "source": [
    "## Aufgabe\n",
    "Was tut das kleine Beispiel?\n",
    "Baue eine Funktion, die einen Array der Länge **n** zurückliefert.\n",
    "Der Inhalt sollen Zufallszahlen mit 2 Nachkommastellen sein die zwischen **from** und **to* liegen."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ed88639-c037-415a-b93f-bcdc8cb49a7c",
   "metadata": {},
   "source": [
    "## Lösung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3ffef006-eac3-41f6-9334-f22db10dc0d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def rand_numbers(n, start, end):\n",
    "    digits = 2; # falls es mal nur 1 oder 3 Nachkommastellen werden sollen\n",
    "    factor = 10 ** digits;\n",
    "    result = []\n",
    "    for i in range(n):\n",
    "        result.append(random.randint(start * factor, end * factor) / factor)\n",
    "        \n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "34cda81b-7611-439e-8ba2-3f01c210fa76",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9.12, 36.56, 4.6, 4.44, 9.67]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rand_numbers(5, 2, 44)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "976b757c-09fa-4492-8996-8129049dc0bf",
   "metadata": {},
   "source": [
    "## Aufgabe\n",
    "\n",
    "Schreibe eine neue Funktion, die diese Funktion als Zinsen in der Funktion zur variablen Zinsberechnung verwendet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "cf269399-9603-4fc6-ae16-c40562d4d8dc",
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "def variabler_zins(anlagebetrag, zinsen):\n",
    "    jahre = len(zinsen)\n",
    "    result = [anlagebetrag]\n",
    "    for i in range(0, jahre):\n",
    "        result.append(result[i] * (1+ zinsen[i]/100))\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "16d443c6-6b7c-4362-9048-92f23f44da3a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[100, 101.49999999999999, 104.03749999999998, 107.67881249999998]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "variabler_zins(100, [1.5, 2.5, 3.5])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebbfb7e2-f7e1-4c1d-9f2e-6b5ad896be11",
   "metadata": {},
   "source": [
    "## Lösung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "ac0de40d-c851-40e8-9f18-2c68c25cd7f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def variabler_zufallszins(anlagebetrag, jahre, min_zins, max_zins):\n",
    "    return variabler_zins(anlagebetrag, rand_numbers(jahre, min_zins, max_zins))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5d41f256-22ff-4604-9680-011cfbe77511",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1000,\n",
       " 1005.5000000000001,\n",
       " 1011.4324500000001,\n",
       " 1024.479928605,\n",
       " 1040.256919505517,\n",
       " 1040.8810736572204]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "variabler_zufallszins(1000, 5, 0, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5af14f52-76be-448b-b15f-2fe0d7d50a13",
   "metadata": {},
   "source": [
    "## Aufgabe\n",
    "Eine einzelne Simulation hat nicht viel Aussagekraft. Schreibe eine Funktion, die die Simulation **n** mal ausführt und von jeder Ausführung das Endergebnis zurückgibt."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4192e1f-8e0d-4de8-b6fb-215849aeb02f",
   "metadata": {},
   "source": [
    "## Lösung"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "e5ef01b5-bdce-4a3e-8d29-a3081126bdab",
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate(anlagebetrag, jahre, min_zins, max_zins, n):\n",
    "    result = []\n",
    "    for i in range(n):\n",
    "        tmp = variabler_zufallszins(anlagebetrag, jahre, min_zins, max_zins)\n",
    "        result.append(tmp[-1]) # letztes Element in Array hat Index -1, vorletztes -2, usw.\n",
    "        \n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "441e6fc3-66e5-41bf-9bb2-c01c475ad0b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1052.6442959071103,\n",
       " 1064.427091942078,\n",
       " 1083.9725955171834,\n",
       " 1089.3384949096728,\n",
       " 1093.7917438123886,\n",
       " 1099.7624262587865,\n",
       " 1112.5348861022283,\n",
       " 1123.567897245912,\n",
       " 1128.9355107957267,\n",
       " 1167.8728995649053]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = simulate(1000, 5, 0, 4, 10)\n",
    "results.sort()\n",
    "results"
   ]
  }
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