Dice_Prob_Rolling_Code_Snippet_2.ipynb

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    "import math\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from matplotlib import figure\n",
    "from ipywidgets import interact\n",
    "from ipywidgets.embed import embed_minimal_html\n",
    "\n",
    "# A single dice \n",
    "def TheDice():\n",
    "    return round(np.random.uniform(low = 0.5, high = 6.5, size = None),0)\n",
    "\n",
    "#n-dice \n",
    "def summingDice(n):\n",
    "    ArrayofDiceoutcomes = np.zeros(n)\n",
    "    for eachdice in range(0,n):\n",
    "        ArrayofDiceoutcomes[eachdice] = TheDice()\n",
    "    return sum(ArrayofDiceoutcomes)\n",
    "\n",
    "#Throws the set of n dice m times and stores the outcome\n",
    "def TheRollingOfDice(m,n):\n",
    "    histo = np.zeros(m)\n",
    "    for i in range(0,m):\n",
    "        histo[i] = summingDice(n)\n",
    "    return histo\n",
    "\n",
    "# Formulates a histogram from the m trials of experimental data \n",
    "#and normalises this to gain a probability distribution\n",
    "def HandMadeHistogram(SimData,minimumofrange,maximumofrange):\n",
    "    numberofInts = []\n",
    "    for i in range(minimumofrange,maximumofrange+1):\n",
    "        numberofsingeint = np.where(SimData == i)[0]\n",
    "        numberofInts.append(len(numberofsingeint))\n",
    "    return [float(x)/sum(numberofInts) for x in numberofInts]\n",
    "\n",
    "\n",
    "# Putting this all together - given the number of trials and the number of dice we can return \n",
    "# the normalised histogram of the distribution of possible sums, the minimum possible and maximum possible sum\n",
    "def FromDiceNumberToData(numberoftrials,numberofdice):\n",
    "    SimData = TheRollingOfDice(numberoftrials,numberofdice)\n",
    "    minimumofrange,maximumofrange = numberofdice,6*numberofdice\n",
    "    HandMadeHist = HandMadeHistogram(SimData,minimumofrange,maximumofrange)\n",
    "    return HandMadeHist,minimumofrange,maximumofrange"
   ]
  }
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