{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "source('./data/ps3prob2data.r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = getprob2data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## a) Mean and standard deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2.554528"
      ],
      "text/latex": [
       "2.554528"
      ],
      "text/markdown": [
       "2.554528"
      ],
      "text/plain": [
       "[1] 2.554528"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#mean survival in years\n",
    "mean(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2.0740803501976"
      ],
      "text/latex": [
       "2.0740803501976"
      ],
      "text/markdown": [
       "2.0740803501976"
      ],
      "text/plain": [
       "[1] 2.07408"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# standard deviation in years\n",
    "sqrt(var(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## b) Frequency histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TAkpggheQyGxBQhJI/BkJgihOQxGZLD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\nQpcEjQoqAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title “Histogram of x”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(x, breaks=seq(0, max(x), 0.1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## c) Data summary\n",
    "The mean survival in the treatment arm (2.5 years) is greater than the baseline mean survival (<1 year). However, the standard deviation in the treatment arm (2.07 years) suggests a large variability in the survival in the treatment arm. The histogram reveals that patients in the treatment arm seem to segregate in two groups: responders and non-responders. The former do not benefit from the treatment at all: almost all of them are dead after 1 year of treatment. The survival of the latter is greatly improved, and most patients survive for longer than the period of the trial. Note that since the study stopped after 5 years, the true mean survival of patients in the treatment arm is certainly more than 2.5 years, and the mean survival of responders even longer.\n",
    "\n",
    "## d) Recommandations for further research\n",
    "Comparing patient data (medical folders, genomics) between responders and non-responders may eludicate a biomarker predictive of response, and a potential intrinsic resistance mechanism in non-responders."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3) \n",
    "The duration of human gestation in days is approximately normally distributed with $N\\sim(280, 8.5^2)$.\n",
    "\n",
    "## a) Graphing the pdf and cdf\n",
    "cdf:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = 280\n",
    "sd = 8.5\n",
    "n_sd = 5\n",
    "quantiles = seq(from = mu-n_sd*sd, to = mu+n_sd*sd, by = 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gCJspNEQf+eL7vRAChSYPIQvCRve27ybaa2eb7spn5b822Tn9smvwgP+7IbDYAi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\nSIAiAUiAIgFIgCIBSIAiAUjw/ytFFyWZ9ahzAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(quantiles, dnorm(quantiles, mean = 280, sd = 8.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "cdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/Xjp23QNnciKtoQxAdWZe/RtAkV+sX6HoHev4SQIqKBswX3VXhTSqepsrdEOyGv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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(quantiles, pnorm(quantiles, mean = 280, sd = 8.5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## b)\n",
    "Probability that the teacher gives birth on or before the day of the final:\n",
    "\n",
    "Due date is May 25, exam is on May 18, therefore there are 25-18 = 7 days between the expected due date and the exam. \n",
    "\n",
    "We are looking for $P(X \\leq \\mu-7) = P(X \\leq 272) = F_X(272)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability that the teacher gives birth on or prior to the exam is 0.1733072"
     ]
    }
   ],
   "source": [
    "cat('The probability that the teacher gives birth on or prior to the exam is', pnorm(272, mean=mu, sd=sd))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## c) \n",
    "Probability that the teacher gives birth in May after the exam is:\n",
    "From the 19th of May (6 days before the mean) to the last day of May (May 31st): 7 days after the mean.\n",
    "\n",
    "We are looking for $P(\\mu-6 \\leq X \\leq \\mu+7) = P(X\\leq \\mu+7)-P(X\\leq \\mu-7)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The probability that the teacher gives birth sometimes after the exam in May is: 0.589793"
     ]
    }
   ],
   "source": [
    "cat('The probability that the teacher gives birth sometimes after the exam in May is:', pnorm(mu+7, mean=mu, sd=sd)-pnorm(mu-7, mean=mu, sd=sd))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## d)\n",
    "Moving the date such that there is a 95\\% chance that the exam falls before the birth:\n",
    "\n",
    "In other words, we compute the probability that the professor gives birth before a certain date with a 5\\% chance.\n",
    "\n",
    "$p = P(X \\leq x)$, we build a grid for x, compute p over values of x via the cdf and pick the first x that yields $p\\leq 0.05$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid = seq(from=mu-24, to = mu, by=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "probs = pnorm(grid, mean=mu, sd = sd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>0.00237490338460939</li><li>0.00340615875995847</li><li>0.00482345299531707</li><li>0.00674455186401385</li><li>0.00931279014370143</li><li>0.0126990229997683</li><li>0.0171024847893373</li><li>0.0227501319481792</li><li>0.0298940554132321</li><li>0.0388066047288512</li><li>0.0497729778022139</li><li>0.0630811988712409</li><li>0.0790096269236994</li><li>0.0978123934346333</li><li>0.119703439398395</li><li>0.144840077867343</li><li>0.173307216251525</li><li>0.20510349934613</li><li>0.240130651376711</li><li>0.278187185213453</li><li>0.318967405295479</li><li>0.36206627019446</li><li>0.406990230208459</li><li>0.453173658141097</li><li>0.5</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0.00237490338460939\n",
       "\\item 0.00340615875995847\n",
       "\\item 0.00482345299531707\n",
       "\\item 0.00674455186401385\n",
       "\\item 0.00931279014370143\n",
       "\\item 0.0126990229997683\n",
       "\\item 0.0171024847893373\n",
       "\\item 0.0227501319481792\n",
       "\\item 0.0298940554132321\n",
       "\\item 0.0388066047288512\n",
       "\\item 0.0497729778022139\n",
       "\\item 0.0630811988712409\n",
       "\\item 0.0790096269236994\n",
       "\\item 0.0978123934346333\n",
       "\\item 0.119703439398395\n",
       "\\item 0.144840077867343\n",
       "\\item 0.173307216251525\n",
       "\\item 0.20510349934613\n",
       "\\item 0.240130651376711\n",
       "\\item 0.278187185213453\n",
       "\\item 0.318967405295479\n",
       "\\item 0.36206627019446\n",
       "\\item 0.406990230208459\n",
       "\\item 0.453173658141097\n",
       "\\item 0.5\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0.00237490338460939\n",
       "2. 0.00340615875995847\n",
       "3. 0.00482345299531707\n",
       "4. 0.00674455186401385\n",
       "5. 0.00931279014370143\n",
       "6. 0.0126990229997683\n",
       "7. 0.0171024847893373\n",
       "8. 0.0227501319481792\n",
       "9. 0.0298940554132321\n",
       "10. 0.0388066047288512\n",
       "11. 0.0497729778022139\n",
       "12. 0.0630811988712409\n",
       "13. 0.0790096269236994\n",
       "14. 0.0978123934346333\n",
       "15. 0.119703439398395\n",
       "16. 0.144840077867343\n",
       "17. 0.173307216251525\n",
       "18. 0.20510349934613\n",
       "19. 0.240130651376711\n",
       "20. 0.278187185213453\n",
       "21. 0.318967405295479\n",
       "22. 0.36206627019446\n",
       "23. 0.406990230208459\n",
       "24. 0.453173658141097\n",
       "25. 0.5\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] 0.002374903 0.003406159 0.004823453 0.006744552 0.009312790 0.012699023\n",
       " [7] 0.017102485 0.022750132 0.029894055 0.038806605 0.049772978 0.063081199\n",
       "[13] 0.079009627 0.097812393 0.119703439 0.144840078 0.173307216 0.205103499\n",
       "[19] 0.240130651 0.278187185 0.318967405 0.362066270 0.406990230 0.453173658\n",
       "[25] 0.500000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "probs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The teacher should pick a date before May 11"
     ]
    }
   ],
   "source": [
    "cat('The teacher should pick a date before May', which(probs>=0.05)[1]-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note the -1 with respect to the first day from which there is more than 5\\% chance that she delivers. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
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   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.3"
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 },
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}