diff options
Diffstat (limited to 'sem6/prob')
| -rw-r--r-- | sem6/prob/stat1/Opgaver.ipynb | 173 | ||||
| -rw-r--r-- | sem6/prob/stat2/opgaver.tex | 23 | ||||
| -rw-r--r-- | sem6/prob/stat3/Untitled.ipynb | 172 |
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 +} |