お年玉問題のシミュレーション

otoshidama.ipynb

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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def get_envelops(p_a):\n",
    "    i = np.random.uniform(0.0, 1.0)\n",
    "    boundary = 0\n",
    "    for money in p_a.keys():\n",
    "        boundary += p_a[money]\n",
    "        if i < boundary:\n",
    "            break\n",
    "    return money, money*2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def run(p_a):\n",
    "    N = 100000\n",
    "    count = 0\n",
    "    total = 0\n",
    "    while count < N:\n",
    "        env_a, env_b = get_envelops(p_a)\n",
    "        if np.random.uniform(0.0, 1.0) < 0.5:\n",
    "            if env_a == 10000:\n",
    "                total += env_b\n",
    "                count += 1\n",
    "        else:\n",
    "            if env_b == 10000:\n",
    "                total += env_a\n",
    "                count += 1\n",
    "    return float(total) / N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12473.6\n",
      "12475.85\n",
      "12466.25\n",
      "12503.3\n",
      "12460.4\n"
     ]
    }
   ],
   "source": [
    "p_a = {5000:1.0/2, 10000:1.0/2}\n",
    "for _ in range(5):\n",
    "    print run(p_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10023.05\n",
      "9987.35\n",
      "10020.5\n",
      "10008.05\n",
      "9986.45\n"
     ]
    }
   ],
   "source": [
    "p_a = {5000:1.0*2/3, 10000:1.0/3}\n",
    "for _ in range(5):\n",
    "    print run(p_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8770.55\n",
      "8718.2\n",
      "8784.65\n",
      "8741.45\n",
      "8773.25\n"
     ]
    }
   ],
   "source": [
    "p_a = {5000:1.0*3/4, 10000:1.0/4}\n",
    "for _ in range(5):\n",
    "    print run(p_a)"
   ]
  }
 ],
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