diff --git a/problem_set_3.ipynb b/problem_set_3.ipynb
new file mode 100644
index 0000000..1fb0e92
--- /dev/null
+++ b/problem_set_3.ipynb
@@ -0,0 +1,165 @@
+{
+ "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": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "R",
+   "language": "R",
+   "name": "ir"
+  },
+  "language_info": {
+   "codemirror_mode": "r",
+   "file_extension": ".r",
+   "mimetype": "text/x-r-source",
+   "name": "R",
+   "pygments_lexer": "r",
+   "version": "3.6.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}