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   "cell_type": "markdown",
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   "source": [
    "# Programmieraufgabe 1  (Geburtstagsparadoxon)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-weight: bold\">Wichtig: Damit alle ben&ouml;tigten Pakete richtig eingebunden werden, f&uuml;hren Sie die n&auml;chste Zelle einmal aus.</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# some setup\n",
    "import numpy as np # makes numpy routines and data types available as np.[name ouf routine or data type]\n",
    "import matplotlib.pyplot as plt # makes plotting command available as plt.[name of command]\n",
    "from numpy import random\n",
    "\n",
    "random.seed(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a) Die Funktion calcchance(size, k, samples) soll die relative H&auml;ufigkeit zur&uuml;ckgeben, dass unter \"size\" vielen Leuten \"k\" Leute am gleichen Tag Geburtstag haben. Das Zufallsexperiment wird dabei \"samples\" oft wiederholt. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calcchance(size=32,k=2,samples=10000):\n",
    "    # if you set parameter=value in the declaration, this becomes the default value \n",
    "    # and the parameter can be omitted on call.\n",
    "    # Everything in the block has to be indented the same amount of spaces (this is\n",
    "    # python's way of { } )\n",
    "           \n",
    "    # loop over the number of samples\n",
    "    for i in range(samples):\n",
    "        # create random birthdays for every person in the group (array of size 'size')\n",
    "        a = random.randint(0,365,size)\n",
    "        # Insert code here ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = calcchance(34,2,10000)\n",
    "print(c)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b) Die folgende Funktion soll die relative H&auml;ufigkeit zur&uuml;ckgeben, dass es unter \"size\" vielen Leuten noch einen weiteren gibt, der am gleichen Tag wie \"num\" Geburtstag hat. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calcchance2(size=32,num=0,samples=10000):\n",
    "    for i in range(samples):\n",
    "        a = random.randint(0,365,size)\n",
    "        # Insert code here\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c) Stellen Sie mittels \"pyplot\" die relativen H&auml;ufigkeiten (10000 Wiederholungen) aus Aufgabe a) graphisch dar (k=2, size = 2,...,90) und geben Sie aus, wie gross die Gruppe sein muss, so dass in \n",
    "\n",
    "(i) 50% \n",
    "(ii) 90%\n",
    "(iii) 95%\n",
    "\n",
    "aller F&auml;lle 2 Leute am selben Tag Geburtstag haben. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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