Blaze rods.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "66f6e4ab-ed9b-4201-8017-8dad029ef502",
   "metadata": {},
   "source": [
    "### Distribution of number of blaze rod drops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "91255e0f-21ed-489a-bccc-3b20815d3b45",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import binom\n",
    "\n",
    "# Set the parameters for the binomial distribution \n",
    "n = 305  # Number of trials\n",
    "p = 0.5  # Probability of success\n",
    "dreams_result = 211\n",
    "\n",
    "# x values\n",
    "x_values = list(range(0, n+1))\n",
    "y_values = [binom.pmf(x, n, p) for x in x_values]\n",
    "\n",
    "# plot the graph\n",
    "plt.bar(x_values, y_values)\n",
    "plt.title(\"Binomial distribution of blaze rod drops\")\n",
    "plt.axvline(dreams_result, color='r', linestyle='--', ymax = 0.5)\n",
    "plt.xlabel(\"Number of blaze rod drops\")\n",
    "plt.ylabel(\"PMF\")\n",
    "plt.text(350, 0.01, \"Red dotted line: The number of blaze rod drops Dream got (211)\", fontsize=8, color='black')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79ba8f98-b0ed-4b21-a5f2-c32e8eb31f08",
   "metadata": {},
   "source": [
    "#### plot for pmf >= some threshold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0e541799-c26f-471e-a62a-51854979520a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#import matplotlib.pyplot as plt\n",
    "#from scipy.stats import binom\n",
    "\n",
    "# Set the parameters for the binomial distribution\n",
    "# n = 305  # Number of trials\n",
    "# p = 0.5  # Probability of success\n",
    "# dreams_result = 211\n",
    "threshold = 0.00005\n",
    "\n",
    "# x values and y values\n",
    "x_values = list(range(0, n+1))\n",
    "y_values = [binom.pmf(x, n, p) for x in x_values]\n",
    "\n",
    "# filter\n",
    "new_x_values = [x for x in x_values if y_values[x] >= threshold]\n",
    "new_y_values = [y for y in y_values if y>= threshold]\n",
    "\n",
    "# plot the graph\n",
    "plt.bar(new_x_values, new_y_values)\n",
    "plt.title(\"Binomial distribution of blaze rod drops\")\n",
    "plt.axvline(dreams_result, color='r', linestyle='--', ymax = 0.5)\n",
    "plt.xlabel(\"Number of blaze rod drops\")\n",
    "plt.ylabel(\"PMF\")\n",
    "plt.text(220, 0.01, \"Red dotted line: The number of blaze rod drops Dream got (211)\", fontsize=8, color='black')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d15fa6ad-a155-438e-a9f3-560534b9691b",
   "metadata": {},
   "source": [
    "#### Code simulation for distribution of blaze rods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "68250648-1e41-446f-9461-5a73b8cda7d9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random\n",
    "from collections import Counter\n",
    "\n",
    "# set the parameters\n",
    "number_of_simulation = 10000\n",
    "data = [] # storing no. of success of each trial, elements could repeat\n",
    "n = 305\n",
    "p = 0.5\n",
    "\n",
    "# simulate data\n",
    "for i in range(number_of_simulation):\n",
    "    success_num = 0\n",
    "    for j in range(n):\n",
    "        if random.random() < p:\n",
    "            success_num += 1\n",
    "    data.append(success_num)\n",
    "\n",
    "# clean up the data\n",
    "dict = Counter(data)\n",
    "x_values = list(dict.keys())\n",
    "y_values = list(y/number_of_simulation for y in dict.values()) # turn frequency into relative frequency\n",
    "\n",
    "max_x = max(x_values)\n",
    "\n",
    "# plot the graph\n",
    "fig = plt.figure(figsize=(12, 8), dpi=80)\n",
    "\n",
    "#plt.bar(x_values, y_values)\n",
    "plt.bar(x_values, y_values, color='blue', alpha=0.5, label='Binomial(305, 1/2) distribution')\n",
    "plt.plot([], [], ' ', label=f\"Maximum number of blaze rod drops out of {number_of_simulation} simulations: {max_x}\")\n",
    "\n",
    "plt.title(f\"Code simulation for blaze rod drops ({number_of_simulation} simulations)\")\n",
    "plt.axvline(dreams_result, color='r', linestyle='--', ymax = 1, label=\"The number of blaze rod drops Dream got (211)\")\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.xlabel(\"Number of blaze rod drops\")\n",
    "plt.ylabel(\"PMF\")\n",
    "#plt.text(220, 0.01, \"Red dotted line: The number of blaze rod drops Dream got (211)\", fontsize=8, color='black')\n",
    "#plt.text(220, 0.005, f\"Maximum number of blaze rod drops out of {number_of_simulation} simulations: {max_x}\", fontsize=8, color='black')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "860cd456-4e46-44ef-82b0-0e06491aaa64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random\n",
    "from collections import Counter\n",
    "\n",
    "# set the parameters\n",
    "number_of_simulation = 10000\n",
    "data = [] # storing no. of success of each trial, elements could repeat\n",
    "n = 305\n",
    "p = 0.5\n",
    "\n",
    "# simulate data\n",
    "for i in range(number_of_simulation):\n",
    "    success_num = 0\n",
    "    for j in range(n):\n",
    "        if random.random() < p:\n",
    "            success_num += 1\n",
    "    data.append(success_num)\n",
    "\n",
    "# clean up the data\n",
    "dict = Counter(data)\n",
    "x_values = list(dict.keys())\n",
    "y_values = list(y/number_of_simulation for y in dict.values()) # turn frequency into relative frequency\n",
    "\n",
    "max_x = max(x_values)\n",
    "\n",
    "# plot the graph\n",
    "fig = plt.figure(figsize=(12, 8), dpi=80)\n",
    "\n",
    "#plt.bar(x_values, y_values)\n",
    "plt.bar(x_values, y_values, color='blue', alpha=0.5, label='Binomial(305, 1/2) distribution')\n",
    "plt.plot([], [], ' ', label=f\"Maximum number of blaze rod drops out of {number_of_simulation} simulations: {max_x}\")\n",
    "\n",
    "plt.title(f\"Code simulation for blaze rod drops ({number_of_simulation} simulations)\")\n",
    "plt.axvline(dreams_result, color='r', linestyle='--', ymax = 1, label=\"The number of blaze rod drops Dream got (211)\")\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.xlabel(\"Number of blaze rod drops\")\n",
    "plt.ylabel(\"PMF\")\n",
    "#plt.text(220, 0.01, \"Red dotted line: The number of blaze rod drops Dream got (211)\", fontsize=8, color='black')\n",
    "#plt.text(220, 0.005, f\"Maximum number of blaze rod drops out of {number_of_simulation} simulations: {max_x}\", fontsize=8, color='black')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8605fb9c-0baf-478d-b2f8-54c81613873c",
   "metadata": {},
   "source": [
    "#### Code simulation for distribution of blaze rods with deduced modified probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "222ab3d1-1b27-4a6e-8687-601ac494da54",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random\n",
    "from collections import Counter\n",
    "import math\n",
    "\n",
    "# set the parameters\n",
    "number_of_simulation = 10000\n",
    "data = [] # storing no. of success of each trial, elements could repeat, every trial has n = 305\n",
    "n = 305\n",
    "p = 0.5\n",
    "m = 1.077881528 # modify constant\n",
    "t = n*p + 3*math.sqrt(n*p*(1-p)) #threshold\n",
    "\n",
    "# simulate data\n",
    "for i in range(number_of_simulation):\n",
    "    success_num = 0\n",
    "    for j in range(n):\n",
    "        if random.random() < p*m:\n",
    "            success_num += 1\n",
    "    data.append(success_num)\n",
    "\n",
    "# clean up the data\n",
    "dict = Counter(data)\n",
    "x_values = list(dict.keys())\n",
    "y_values = list(y/number_of_simulation for y in dict.values()) # turn frequency into relative frequency\n",
    "\n",
    "max_x = max(x_values)\n",
    "\n",
    "# plot the threshold and % of distribution less than the threshold\n",
    "sum = 0\n",
    "for x,y in dict.items():\n",
    "    if x <= t:\n",
    "        sum += y\n",
    "unsuspicious_percentage = sum/number_of_simulation\n",
    "plt.axvline(t, color='r', linestyle='--', ymax = 0.5)\n",
    "plt.text(220, 0.01, f\"Red dotted line: The threshold, {t:.3f}\", fontsize=8, color='black')\n",
    "plt.text(220, 0.005, f\"Percentage of unsuspicious (modified) distribution: {unsuspicious_percentage}\", fontsize=8, color='black')\n",
    "#plt.text(220, 0.005, f\"Maximum number of blaze rod drops out of {number_of_simulation} simulations: {max_x}\", fontsize=8, color='black')\n",
    "\n",
    "# plot the graph\n",
    "plt.bar(x_values, y_values)\n",
    "plt.title(f\"Code simulation for modified blaze rod drops ({number_of_simulation} simulations)\")\n",
    "plt.xlabel(\"Number of blaze rod drops\")\n",
    "plt.ylabel(\"PMF\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d45573ad-81ca-46cc-92cc-9c757a7dadac",
   "metadata": {},
   "outputs": [],
   "source": [
    "#### calculations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d76e8faf-57a8-4cff-89f8-0e18fe6b56b4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "178.69637379485948\n",
      "[23462.54768838695, -54914.98938420604, 31932.394007432144]\n",
      "[1.26265668 1.07788153]\n",
      "(1.0778815282379226+0j) (1.262656682426507+0j)\n"
     ]
    }
   ],
   "source": [
    "n = 305\n",
    "p = 0.5\n",
    "t = n*p + 3*math.sqrt(n*p*(1-p))\n",
    "print(t)\n",
    "k = 1.644853627**2\n",
    "\n",
    "import numpy as np\n",
    "coef = []\n",
    "coef.append(152.5**2 + k*76.25)\n",
    "coef.append(-2*t*152.5-k*152.5)\n",
    "coef.append(t**2)\n",
    "\n",
    "print(coef)\n",
    "print(np.roots(coef))\n",
    "\n",
    "\n",
    "a = coef[0]\n",
    "b = coef[1]\n",
    "c = coef[2]\n",
    "\n",
    "# calculate the discriminant\n",
    "import cmath\n",
    "d = (b**2) - (4*a*c)\n",
    "\n",
    "sol1 = (-b-cmath.sqrt(d))/(2*a)\n",
    "sol2 = (-b+cmath.sqrt(d))/(2*a)\n",
    "print(sol1, sol2)\n",
    "\n"
   ]
  }
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