Added assignments for prob

3 files changed, 368 insertions, 0 deletions

diff --git a/sem6/prob/stat1/Opgaver.ipynb b/sem6/prob/stat1/Opgaver.ipynb
new file mode 100644
index 0000000..b398bfa
--- /dev/null
+++ b/sem6/prob/stat1/Opgaver.ipynb
@@ -0,0 +1,173 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import scipy.stats\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Problem 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Create data\n",
+    "c = [ 112, 121, 126, 108, 141, 104, 136, 134,\n",
+    "  121, 118, 143, 116, 108, 122, 127, 140,\n",
+    "  113, 117, 126, 130, 134, 120, 131, 133,\n",
+    "  118, 125, 151, 147, 137, 140, 132, 119,\n",
+    "  110, 124, 132, 152, 135, 130, 136, 128 ]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Len: 40\n",
+      "Mean: 127.425\n",
+      "Median: 127.5\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Opgave A\n",
+    "print(f\"Len: {len(c)}\")\n",
+    "print(f\"Mean: {np.mean(c)}\")\n",
+    "print(f\"Median: {np.median(c)}\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7fa0b92dae80>]"
+      ]
+     },
+     "execution_count": 38,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Opgave B\n",
+    "sigma = np.std(c)\n",
+    "mean = np.mean(c)\n",
+    "\n",
+    "# Calculate a normal fitting\n",
+    "x = np.linspace(mean - 3*sigma, mean + 3 * sigma, 100)\n",
+    "\n",
+    "plt.hist(c, 20, density=True)\n",
+    "plt.plot(x, scipy.stats.norm.pdf(x, mean, sigma))\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Stddiv: 11.723667301659493\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Opgave C\n",
+    "print(f\"Stddiv: {sigma}\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 68,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Percent in interval: 85.0%\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Opgave D\n",
+    "r = 1.5 * sigma\n",
+    "inside = ((c > (mean - r)) & (c < (mean + r))).sum()\n",
+    "percent = 100 * inside / len(c)\n",
+    "print(f\"Percent in interval: {percent}%\")"
+   ]
+  },
+  {
+   "cell_type": "raw",
+   "metadata": {},
+   "source": [
+    "# Opgave F\n",
+    "This fits well with 85 between 68 and 95"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Problem 2"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/sem6/prob/stat2/opgaver.tex b/sem6/prob/stat2/opgaver.tex
new file mode 100644
index 0000000..0596cce
--- /dev/null
+++ b/sem6/prob/stat2/opgaver.tex
@@ -0,0 +1,23 @@
+\title{Opgaver til Statistics Module 2}
+
+\section{Exercise 2}
+
+\subsection{Opgave A}
+
+Her kan vi sige at $y_i \sim \mathcal{N}(S', \sigma^2)$ hvor $S' = \alpha S$ og derfor er det at estimere $S'$ og isolere for $d$.
+
+Først kan vi estimere for $S'$, og eftersom $y_i$ er normal fordelt kan man estimere mean $S'$ med: \[
+    \hat{\mu} = \sum_{i=1}^{n} \frac {x_i} n
+.\] 
+
+Nu kan vi isolere for $d$.
+\begin{align*}
+    S' = \hat{\mu} = S \cdot \frac {0.5} d = \frac 1 n \sum_{i=1}^{n} x_i \\
+    d = S \cdot \frac{0.5 n}{\sum_{i=1}^{n} x_i}
+\end{align*}
+
+\section{Exercise 3}
+
+\subsection{Part 1}
+
+Okay jeg fortsætter på papir.
diff --git a/sem6/prob/stat3/Untitled.ipynb b/sem6/prob/stat3/Untitled.ipynb
new file mode 100644
index 0000000..b846ff4
--- /dev/null
+++ b/sem6/prob/stat3/Untitled.ipynb
@@ -0,0 +1,172 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "from scipy.stats import norm\n",
+    "from IPython.display import display, Math, Markdown\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Opgaver\n",
+    "\n",
+    "Har lavet problem 1 på papir, men vil lave resten i python da det nok er lidt lettere."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Problem 2\n",
+    "\n",
+    "Går ud fra at PCB er i ppm, og kalder den $\\theta$.\n",
+    "\n",
+    "$$\n",
+    "X_i = \\theta + W_i\n",
+    "$$\n",
+    "hvor $W_i \\sim \\mathcal{N}(\\mu, \\sigma^2)$, $\\sigma = 0.08$.\n",
+    "Her går jeg ud fra at $\\mu = 0$.\n",
+    "\n",
+    "Derfor er: \n",
+    "$$\n",
+    "E[X] = \\theta\n",
+    "$$\n",
+    "og\n",
+    "$$\n",
+    "Var[X] = (0.08)^2\n",
+    "$$\n",
+    "\n",
+    "Kan sige at confidence level er:\n",
+    "$$\n",
+    "[\\bar{X} - z_{\\frac \\alpha 2} \\cdot \\frac \\sigma {\\sqrt{n}}, \\bar{X} + z_{\\frac \\alpha 2} \\cdot \\frac \\sigma {\\sqrt{n}}]\n",
+    "$$\n",
+    "with probability $1-\\alpha$.\n",
+    "Her er \n",
+    "$$\n",
+    "z_p = \\Phi^{-1}(1 - p)$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "samples = [11.2, 12.4, 10.8, 11.6, 12.5, 10.1, \n",
+    "           11.0, 12.2, 12.4, 10.6]\n",
+    "n = len(samples)\n",
+    "\n",
+    "X_bar = np.mean(samples)\n",
+    "sigma = 0.08"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle P(11.430416397415636 \\leq \\theta \\leq 11.529583602584365) = 0.95$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Math object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Del A\n",
+    "alpha = 0.05\n",
+    "Z = norm.ppf(1 - alpha/2)\n",
+    "\n",
+    "dist = Z * sigma / np.sqrt(n)\n",
+    "lower = X_bar - dist\n",
+    "upper = X_bar + dist\n",
+    "\n",
+    "display(Math(f\"P({lower} \\\\leq \\\\theta \\\\leq {upper}) = {1 - alpha}\"))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle [-\\infty, 11.529583602584365]$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Math object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "\n",
+    "# Okay så lower confidence level er åbenbart at man går fra -infty til upper limit\n",
+    "\n",
+    "display(Math(f\"[-\\\\infty, {upper}]\"))\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle [11.430416397415636, \\infty]$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Math object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Del C\n",
+    "# Og igen for uppwer\n",
+    "\n",
+    "display(Math(f\"[{lower}, \\\\infty]\"))"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}