1231 lines
371 KiB
Plaintext
1231 lines
371 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "fd2f3bf7-b314-4449-95dc-f07d1a13f1c6",
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"metadata": {
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"nbgrader": {
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"grade": false,
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"grade_id": "cell-04300aa5f61f7f12",
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"locked": true,
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}
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},
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"source": [
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"# 5. Programmierübung: SciPy\n",
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"\n",
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"<div style=\"display:flex;\">\n",
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" <div style=\"text-align: left\">\n",
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" Willkommen zur fünften Programmierübung Einführung in Python 3.\n",
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" </div>\n",
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" <img style=\"float: right; margin: 0px 15px 15px 0px\" src=\"https://www.python.org/static/img/python-logo-large.c36dccadd999.png?1576869008\" width=\"100\" />\n",
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"</div>\n",
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"\n",
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"Wenn Sie Fragen oder Verbesserungsvorschläge zum Inhalt oder Struktur der Notebooks haben, dann können sie eine E-Mail an Phil Keier ([p.keier@hbk-bs.de](mailto:p.keier@hbk-bs.de?subject=[SigSys]%20Feedback%20Programmierübung&)) oder Martin Le ([martin.le@tu-bs.de](mailto:martin.le@tu-bs.de?subject=[SigSys]%20Feedback%20Programmierübung&)) schreiben.\n",
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"\n",
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"Link zu einem Python Spickzettel: [hier](https://s3.amazonaws.com/assets.datacamp.com/blog_assets/PythonForDataScience.pdf)\n",
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"\n",
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"Der Großteil des Python-Tutorials stammt aus der Veranstaltung _Deep Learning Lab_ und von [www.python-kurs.eu](https://www.python-kurs.eu/python3_kurs.php) und wurde für _Signale und Systeme_, sowie _Einführung in die Programmierung für Nicht Informatiker_ angepasst.\n",
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"\n",
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"---"
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]
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},
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{
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"cell_type": "markdown",
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"id": "bb677cea-65c2-486d-9442-6495b5063bd2",
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"metadata": {
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"nbgrader": {
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"grade": false,
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"grade_id": "cell-110034393ecbe731",
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"locked": true,
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"schema_version": 3,
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"solution": false,
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}
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},
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"source": [
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"# Was ist SciPy\n",
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"\n",
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"SciPy steht für Scientific Python und ist eine Open-Source-Bibliothek, die auf der bewährten Architektur von NumPy aufbaut. Sie bietet eine Vielzahl von Funktionen, die speziell für ingenieurtechnische und wissenschaftliche Anwendungen entwickelt wurden. In diesem Zusammenhang möchten wir uns insbesondere mit Teilen des Statistikmoduls von SciPy vertraut machen.\n",
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"\n",
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"__Für dieses Notebook schauen Sie bitte in die [SciPy Docs](https://docs.scipy.org/doc/scipy/tutorial/index.html)!!!__ Dort sind alle Funktionen beschrieben die wir hier bearbeiten und noch mehr!\n",
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"\n",
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"---"
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]
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},
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{
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"cell_type": "markdown",
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"id": "3dde4289-bc10-49fc-875d-ebc44fbf807a",
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"metadata": {
|
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|
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"nbgrader": {
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"grade": false,
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"grade_id": "cell-82f61f58224c5db9",
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"locked": true,
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"schema_version": 3,
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"solution": false,
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"task": false
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}
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},
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"source": [
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"SciPys wird meist als `sp` importiert da für diese Aufgabe nur das Statistik modul nötig ist wird einfach dieses importiert. Aufgrund des kurzen schlüssigen namens findet keine umbenennung statt:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"id": "e058b67a-ab34-4685-b023-084bfa80f171",
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"metadata": {
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"nbgrader": {
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"grade": false,
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"grade_id": "cell-fe3ab9d39498717f",
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"locked": true,
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"schema_version": 3,
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"solution": false,
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"task": false
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}
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},
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"outputs": [],
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"source": [
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"from scipy import stats"
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]
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},
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{
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"cell_type": "markdown",
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"id": "57ada7f0-5eea-45cc-b8d0-85f52c7f6b55",
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"metadata": {
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"nbgrader": {
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"grade": false,
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"grade_id": "cell-eec41b75718f0e4e",
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"locked": true,
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"schema_version": 3,
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"solution": false,
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"task": false
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}
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},
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|
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"source": [
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|
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"---"
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]
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},
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{
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"cell_type": "markdown",
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"id": "5983dc91-91f3-4b6b-b6c2-9873b9ea8db9",
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|
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"metadata": {
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"nbgrader": {
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"grade": false,
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"grade_id": "cell-65e8f06a2b373c8c",
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"locked": true,
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"schema_version": 3,
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"solution": false,
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"task": false
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}
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},
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"source": [
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|
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"# Lineare Regression\n",
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"\n",
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|
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"## Motivation\n",
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"\n",
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"Die **lineare Regression** ist eine grundlegende Methode zur Modellierung von Beziehungen zwischen Variablen. Sie hilft, Zusammenhänge zu verstehen und ermöglicht Vorhersagen auf Basis vorhandener Daten. Durch die Bestimmung einer linearen Beziehung zwischen einer abhängigen und einer oder mehreren unabhängigen Variablen können wir Trends identifizieren und zukünftige Werte schätzen. Ihre Einfachheit, Effizienz und die Möglichkeit, auch bei großen Datensätzen präzise Ergebnisse zu erzielen, machen sie zu einem wertvollen Werkzeug in der Datenanalyse und ein Fundament für komplexere Modelle.\n",
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"\n",
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"Dafür geht man davon aus, dass es zwei unabhängige Variablen $x_1$ & $x_2$ gibt, für die eine Zukünftige Aussage getätigt werden soll. Hierfür wird eine fehlerminimierte Gerade $g(x)$ zwischen die Datenpunkte gelegt. Daraus resultierenden lässt sich mit $g(x)$ eine zukünftige Vorhersage in einem bestimmten Fehlerbereich tätigen.\n",
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"\n",
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"Aus der Schule sollte die Geraden Gleichung $g(x) = m\\cdot x+b$ bekannt sein. Dabei beschreibt $m$ die Steigung (Slope) & $b$ den Schnittpunkt mit der y-Achse (interception). Die **lineare regression** bietet daher die Möglichkeit diese beiden Parameter herauszufinden.\n",
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"\n",
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"Für das folgende Beispiel werden zwei (pseudo-)zufällig erzeugte Datensets generiert, auf welche dann die lineare regression angewandt wird. "
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]
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},
|
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|
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{
|
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|
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"cell_type": "code",
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|
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"execution_count": 1,
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|
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"id": "60712a1d-7a55-44f4-89e9-cae5ceab952a",
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|
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"metadata": {
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"nbgrader": {
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"grade": false,
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"grade_id": "cell-fbb9bfd35036d55e",
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"locked": true,
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"schema_version": 3,
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"solution": false,
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"task": false
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}
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},
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"outputs": [
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|
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{
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|
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"data": {
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"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
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"<Figure size 640x480 with 1 Axes>"
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|
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]
|
||
|
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},
|
||
|
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"metadata": {},
|
||
|
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"output_type": "display_data"
|
||
|
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}
|
||
|
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],
|
||
|
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"source": [
|
||
|
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"import numpy as np\n",
|
||
|
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"import matplotlib.pyplot as plt\n",
|
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|
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"\n",
|
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|
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"rand = np.random.default_rng(42) # RNG with fixed seed\n",
|
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"\n",
|
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|
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"# Generate, Scale, round and sort random numbers for an increasing slope\n",
|
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"scalar: int = 10\n",
|
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"x: np.array = np.round(np.sort(rand.random(20) * scalar), decimals=2)\n",
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"y: np.array = np.round(np.sort(rand.random(20) * scalar), decimals=2)\n",
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"\n",
|
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|
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"# Plot these values\n",
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"plt.title(\"Scattered Random Values\")\n",
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|
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"plt.grid()\n",
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"plt.xlabel(\"X\")\n",
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|
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"plt.ylabel(\"Y\")\n",
|
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|
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"plt.scatter(x,y, color='g')\n",
|
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|
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"plt.show()"
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]
|
||
|
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},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "083ba4ea-8e6f-4286-8049-1c8e3f22c004",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
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"grade": false,
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"grade_id": "cell-caa85fe6a76214bf",
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|
"locked": true,
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"schema_version": 3,
|
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"solution": false,
|
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|
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"task": false
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}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"Aus den erzeugten Daten ist klar ersichtlich, dass diese einem Trend folgen. Mittels SciPy wollen wir diesen Trend darstellen.\n",
|
||
|
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"\n",
|
||
|
|
"Dazu wird die Funktion `linregress` verwendet. Diese verlangt, wie aus der [Dokumentation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.linregress.html#scipy.stats.linregress) zu entnehmen, zwei arrays mit Daten. \n",
|
||
|
|
"\n",
|
||
|
|
"Die Ausgabe ist aufgespalten in 5 Parameter:\n",
|
||
|
|
"- slope: die Steigung `m` der Geraden\n",
|
||
|
|
"- intercept: der Punkt an dem die Gerade die y-Achse trifft oder das `b`\n",
|
||
|
|
"- rvalue: der Pearson Korrelations Koefficient, welcher voerst ignoriert wird\n",
|
||
|
|
"- pvalue: der p-Wert das die Nullhypothese stimmt, wird auch ignoriert\n",
|
||
|
|
"- stderr: der Standard Error der Steigung, unter der Annahme einer Normalverteilung der Daten *(PCGs sind Normalverteilt)*"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 47,
|
||
|
|
"id": "9c1959d8-5bac-45fa-9aa2-47fa79943d72",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-553a583b633273d5",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"slope, intercept, _, _, stderr = stats.linregress(x,y)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "2c2bd060-bb4c-440f-9a04-72382c9a33eb",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-111845c39238eeee",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"Aus `slope` & `intercept` lässt sich folglich eine Gerade definieren:"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 52,
|
||
|
|
"id": "1e30868c-f11f-43bd-a60b-200ec00e903f",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-49d79f2b8dcf7315",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"def line(x: float) -> float:\n",
|
||
|
|
" '''\n",
|
||
|
|
" Evaluates the rounded line from the previous\n",
|
||
|
|
" evaluated linear regression model\n",
|
||
|
|
"\n",
|
||
|
|
" Note: Output rounded to 2 decimal places\n",
|
||
|
|
" '''\n",
|
||
|
|
" res: float = slope * x + intercept\n",
|
||
|
|
" rounded: np.float64 = np.round(res, decimals=2)\n",
|
||
|
|
" return float(rounded)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "8fdd9724-5c61-471d-a121-787f2d56f132",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-a63e440ba0b57186",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"Diese kann über den gesatme bereich dargestellt werden. Dazu werden die bereits bekannten x-Werte verwendet:"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 67,
|
||
|
|
"id": "0a59d146-4ae3-429a-a67e-7c158d5ebac7",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-5239bfcad5788ae3",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"# Calculate the Line using vectorization\n",
|
||
|
|
"regline: np.array = np.vectorize(line)(x)\n",
|
||
|
|
"\n",
|
||
|
|
"# Plot tvalues\n",
|
||
|
|
"plt.title(\"Scattered Random Values\")\n",
|
||
|
|
"plt.grid()\n",
|
||
|
|
"\n",
|
||
|
|
"plt.xlabel(\"X\")\n",
|
||
|
|
"plt.ylabel(\"Y\")\n",
|
||
|
|
"\n",
|
||
|
|
"plt.scatter(x,y, color='g', label=\"Original Data\")\n",
|
||
|
|
"plt.plot(x, regline, color='m', label=\"Fitted line\")\n",
|
||
|
|
"\n",
|
||
|
|
"plt.legend()\n",
|
||
|
|
"\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "802bf60a-e402-4912-96bf-baa6cd398c6e",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-e0da661ffad2086e",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"Mit diesem Model lässt sich dementsprechend die \"Zukunft\" vorhersagen. Hierfür können wir im folgenden einfach die Werte für `-1` & `11` berechnen und diese dem Plot hinzufügen:"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 89,
|
||
|
|
"id": "e62f6248-5813-4df0-9715-a72d3a5467f8",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-92a5bbb041e28a56",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"# Future Values\n",
|
||
|
|
"fut: np.array = np.array([line(-1), line(11)])\n",
|
||
|
|
"\n",
|
||
|
|
"# Calculate extended Line using vectorization\n",
|
||
|
|
"ext_range: np.array = np.arange(-1,12)\n",
|
||
|
|
"regline: np.array = np.vectorize(line)(ext_range)\n",
|
||
|
|
"\n",
|
||
|
|
"# Plot values\n",
|
||
|
|
"plt.title(\"Scattered Random Values\")\n",
|
||
|
|
"plt.grid()\n",
|
||
|
|
"\n",
|
||
|
|
"plt.xlabel(\"X\")\n",
|
||
|
|
"plt.ylabel(\"Y\")\n",
|
||
|
|
"\n",
|
||
|
|
"plt.scatter(x,y, color='g', label=\"Original Data\")\n",
|
||
|
|
"plt.plot(ext_range, regline, color='m', label=\"Fitted Line\")\n",
|
||
|
|
"plt.scatter((-1, 11), fut, color='r', label=\"Predicted Data\")\n",
|
||
|
|
"\n",
|
||
|
|
"plt.legend()\n",
|
||
|
|
"\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "04f002a5-4339-4225-9515-848513347697",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-6c8576c776d11325",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"Wie zu erwarten liegen beide Werte auf der Geraden.\n",
|
||
|
|
"\n",
|
||
|
|
"Um deren Werte zu ermitteln lassen sich diese mittels print einfach ausgeben, dies sollte immer mit Angabe des Standard Errors erfolgen. Sonst ist unklar wie genau die Daten sind:"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 94,
|
||
|
|
"id": "563d452b-350c-4628-a97d-5d9ce268f4c4",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-7677ec5dda3e8e13",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"Prediction of f(11) = 10.16, with standard deviation 0.07\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"print(\"Prediction of f(11) = {}, with standard deviation {}\".format(line(11), np.round(stderr, decimals=2)))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "5e81b1a9-4155-4bfd-8613-2530dbe61f03",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-facd8e8ef9f4aed1",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"### Aufgabe\n",
|
||
|
|
"\n",
|
||
|
|
"*7 Punkte*\n",
|
||
|
|
"\n",
|
||
|
|
"Bestimme mittels Linearer Regression die *best fit* Funktion für die beiden gegebenen Datensets `x_data` & `y_data`, unter beachtung folgender Punkte:\n",
|
||
|
|
"\n",
|
||
|
|
"- Plotte das Ergebnis angemessen\n",
|
||
|
|
"- Nutze SciPys `linregress` Funktion, speichere den Output vor dem entpacken in der Variablen `l`\n",
|
||
|
|
"- Definiere die Funktion `reg_line` mit einem Eingabeparameter\n",
|
||
|
|
"- Bestimme die Werte für `-0.3` & `3.4` speichere diese als liste in variablen `future`\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 147,
|
||
|
|
"id": "f5b801bc-450e-417b-aeea-9b69d638fb64",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-cb5b277089c75c40",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"import numpy as np\n",
|
||
|
|
"random = np.random.default_rng(420)\n",
|
||
|
|
"\n",
|
||
|
|
"# 2 scuffed up One-Liners :)\n",
|
||
|
|
"x_data: np.array = np.sort(np.round(random.random(40)*np.pi, decimals=2))\n",
|
||
|
|
"y_data: np.array = np.flip(np.sort(np.round(random.random(40)*np.sqrt(2), decimals=2)))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 155,
|
||
|
|
"id": "2645541f-c30f-487e-be65-3ec5ac22d427",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-12b5b631856ffe41",
|
||
|
|
"locked": false,
|
||
|
|
"points": 1,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"# BEGIN SOLUTION\n",
|
||
|
|
"l = stats.linregress(x_data,y_data)\n",
|
||
|
|
"slope, intercept, _, _, stderr = l\n",
|
||
|
|
"\n",
|
||
|
|
"def reg_line(x: float) -> float:\n",
|
||
|
|
" return float(np.round(slope*x+intercept,decimals=2))\n",
|
||
|
|
"\n",
|
||
|
|
"ext: tuple = (-0.3, 3.4)\n",
|
||
|
|
"rl: np.array = np.vectorize(reg_line)(ext)\n",
|
||
|
|
"\n",
|
||
|
|
"future: list = [reg_line(ext[0]), reg_line(ext[1])]\n",
|
||
|
|
"# Plot values\n",
|
||
|
|
"plt.title(\"Scattered Random Values\")\n",
|
||
|
|
"plt.grid()\n",
|
||
|
|
"\n",
|
||
|
|
"plt.xlabel(\"X\")\n",
|
||
|
|
"plt.ylabel(\"Y\")\n",
|
||
|
|
"\n",
|
||
|
|
"plt.scatter(x_data,y_data, color='g', label=\"Original Data\")\n",
|
||
|
|
"plt.plot(ext, rl, color='m', label=\"Fitted Line\")\n",
|
||
|
|
"plt.scatter(ext, future, color='r', label=\"Predicted Data\")\n",
|
||
|
|
"\n",
|
||
|
|
"plt.legend()\n",
|
||
|
|
"\n",
|
||
|
|
"plt.show()\n",
|
||
|
|
"# END SOLUTION"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 154,
|
||
|
|
"id": "aa34ed84-f200-4863-be0b-40ff5492c654",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-8f20c3645d0a9b46",
|
||
|
|
"locked": true,
|
||
|
|
"points": 6,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# Hier werden ihre Lösungen getestet\n",
|
||
|
|
"\n",
|
||
|
|
"# Check if reg_line is defined\n",
|
||
|
|
"assert 'reg_line' in dir()\n",
|
||
|
|
"\n",
|
||
|
|
"# Check if reg_line gives right output\n",
|
||
|
|
"assert reg_line(10) == -3.04\n",
|
||
|
|
"\n",
|
||
|
|
"# Check if future values are calculated right\n",
|
||
|
|
"assert future == [1.51, -0.12]\n",
|
||
|
|
"\n",
|
||
|
|
"### BEGIN HIDDEN TESTS\n",
|
||
|
|
"sl, ip, _, _, se = stats.linregress(x_data,y_data)\n",
|
||
|
|
"slope, intercept, _, _, stderr = l\n",
|
||
|
|
"\n",
|
||
|
|
"assert slope == sl\n",
|
||
|
|
"assert intercept == ip\n",
|
||
|
|
"assert stderr == se\n",
|
||
|
|
"\n",
|
||
|
|
"### END HIDDEN TESTS"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "8369e788-5862-488b-a003-d3cd31ebaa99",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-59872a1e95590378",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"---"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "02656b99-d250-4a21-bc2d-46007806d81d",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-455ed6a04d0d701f",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"# Verteilungen\n",
|
||
|
|
"\n",
|
||
|
|
"## Probability Density Function - Normal Verteilung\n",
|
||
|
|
"\n",
|
||
|
|
"### Motivation\n",
|
||
|
|
"\n",
|
||
|
|
"Es wurden Daten über die Körperlänge eines Bienenvolkes erhoben, dementsprechend liegen diskrete Werte über die deren Körperlängen vor. Logischerweise repräsentiert dies nur das erhobene Bienenvolk, dieses arbeitet aber kontinuierlich weiter und erzeugt nachkommen. Die Population verändert sich. \n",
|
||
|
|
"\n",
|
||
|
|
"Daher ist anzunehmen, dass auch Werte zwischen den bereits Erhobenen auftreten können. Um dies zu Modellieren wird eine Normalverteilung benötigt.\n",
|
||
|
|
"\n",
|
||
|
|
"Schauen wir uns dazu erst die Gaussche Normalverteilung an, diese hat ihren Mittelpunkt bei $x=0$, bezeichnet als Erwartungswert $\\mu$, und eine Standardabweichung $\\sigma = 1$. Mathematisch ist sie definiert als $$p(x|\\mu,\\sigma)=\\frac{1}{\\sqrt(2\\pi\\sigma^2)}e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}$$\n",
|
||
|
|
"\n",
|
||
|
|
"SciPy bietet hierfür das `norm` objekt aus dem `stats` Modul an, dieses verlangt die beiden Parameter $\\mu$ & $\\sigma$, das auf dem `norm` Objekt kann dann die Funktion `pdf` mit einem Paramter als Stepsize oder einem Array aufgerufen werden. Nach Plotten ergibt sich folglich die Normalverteilung (von -4 bis 4):"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 23,
|
||
|
|
"id": "2803dcac-bb3b-4aff-a3c9-c0085148c376",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-54174b5f7d8309db",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"x = np.arange(-4, 4, 0.01) # Plot between -4 and 4 with stepsize 0.01\n",
|
||
|
|
"y = stats.norm(0,1).pdf(x) # Calculate pdf with mu=0, sigma=1\n",
|
||
|
|
"\n",
|
||
|
|
"# Plot\n",
|
||
|
|
"plt.title(\"Gaussche Normalverteilung\")\n",
|
||
|
|
"plt.plot(x, y)\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "ca2f768f-16ff-47ff-b898-fe0b8cf3511f",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-259b8d6cb9d76981",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"Um herauszufinden wie viel Prozent einer Population innerhalb dieser Normalverteilung fallen wird die Funktion `ppf` (Percent Point Function) verwendet.\n",
|
||
|
|
"\n",
|
||
|
|
"Am Beispiel 90% der Population:"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 47,
|
||
|
|
"id": "0e5e7709-90a2-4a30-b49f-cbb243aa4e4b",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-5a9ed9588ce2ea27",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"90% of the Population fall into the range 1.282.\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"percentile = stats.norm(0,1).ppf(0.9)\n",
|
||
|
|
"print(f\"90% of the Population fall into the range {percentile:0.3f}.\")"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "96afa424-d697-4c60-aa9b-4655491f4f13",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-5102a53fda328278",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"Um dies zu veranschaulichen:"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 21,
|
||
|
|
"id": "4f5d7f54-856f-4e12-8251-d0cdc5c0f002",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-5d84b05b2808a672",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 900x600 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"fig, ax = plt.subplots(figsize=(9,6))\n",
|
||
|
|
"ax.plot(x,y, color='r')\n",
|
||
|
|
"\n",
|
||
|
|
"# filling under the curve\n",
|
||
|
|
"x_fill = np.arange(-4, percentile, 0.01)\n",
|
||
|
|
"y_fill = stats.norm(0,1).pdf(x_fill)\n",
|
||
|
|
"ax.fill_between(x_fill, y_fill, 0, color='g')\n",
|
||
|
|
"plt.title(\"Filled Percentile under Normal Curve\")\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "1f7a26f6-36d8-4561-ad68-db6c19c7720e",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-c469fe12a69725b1",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"Machen wir dies alles am Beispiel der Fuchsrote Lockensandbiene fest. Diese ist laut [Bundesministerium für Ernährung und Landwirtschaft](https://www.bmel.de/DE/themen/landwirtschaft/artenvielfalt/bienen-fuettern/wildbienen-honigbienen-und-co.html) 12-14 mm groß. Daher lässt sich annehmen das die meisten Bienen $\\mu=13mm$, mit einer Standardabweichung von $\\sigma=1mm$ haben. Wir wollen nun wissen wie groß 95% der Bienen sind, rechnen wir dies mittels `ppf` aus:"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 103,
|
||
|
|
"id": "6d57bdf0-8e75-4760-8159-d42effd9ea62",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-360e11812d2e9932",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 900x600 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"mu = 13 # Mean\n",
|
||
|
|
"sigma = 1 # std deviation in mm\n",
|
||
|
|
"\n",
|
||
|
|
"x_norm = np.linspace(10, 16, 100) # Normaldistribution range from 10-16mm \n",
|
||
|
|
"y_norm = stats.norm(mu, sigma).pdf(x) # Calculate normal\n",
|
||
|
|
"\n",
|
||
|
|
"# Height of 95th percentile of bees\n",
|
||
|
|
"percentile = stats.norm(mu,sigma).ppf(0.95)\n",
|
||
|
|
"\n",
|
||
|
|
"x_percentile = np.arange(x_norm[0], percentile, 0.01)\n",
|
||
|
|
"y_percentile = stats.norm(mu,sigma).pdf(x_percentile)\n",
|
||
|
|
"\n",
|
||
|
|
"# Plot\n",
|
||
|
|
"fig, ax = plt.subplots(figsize=(9,6))\n",
|
||
|
|
"ax.plot(x_norm, y_norm, color='r')\n",
|
||
|
|
"\n",
|
||
|
|
"# filling under the curve\n",
|
||
|
|
"ax.fill_between(x_percentile, y_percentile, 0, alpha=0.2, color='#FE0000')\n",
|
||
|
|
"\n",
|
||
|
|
"\n",
|
||
|
|
"# Set text\n",
|
||
|
|
"ax.text(0.5,0.25,\n",
|
||
|
|
" f\"95th percentile of bees fall under {percentile:.2f}mm\",\n",
|
||
|
|
" ha='center', va='center', transform=ax.transAxes,\n",
|
||
|
|
" bbox={'facecolor':'#fafafa','alpha':1,'edgecolor':'none','pad':1},\n",
|
||
|
|
" color='#de2e0b'\n",
|
||
|
|
" )\n",
|
||
|
|
"\n",
|
||
|
|
"# Show\n",
|
||
|
|
"plt.title(\"Filled Percentile under Normal Curve\")\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "e9c59eb8-bfb1-46f2-bf1f-af1ffe59e190",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-7718d285f36c2fad",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"source": [
|
||
|
|
"### Aufgabe \n",
|
||
|
|
"\n",
|
||
|
|
"*6 Punkte*\n",
|
||
|
|
"\n",
|
||
|
|
"Gegeben sind die nach Altersgruppe aufgeschlüsselten Durschnittskörpergrößen (in cm) von Frauen in Deutschland. (Zu finden beim [Statistischen Bundesamt](https://www.destatis.de/DE/Themen/Gesellschaft-Umwelt/Gesundheit/Gesundheitszustand-Relevantes-Verhalten/Tabellen/koerpermasse-frauen.html))\n",
|
||
|
|
"\n",
|
||
|
|
"Gehe wie folgt vor:\n",
|
||
|
|
"\n",
|
||
|
|
"- Berechne das arithmetische Mittel nutze dafür NumPy. und speichere das Ergebnis mit einer Genauigkeit von 1 Dezimalstelle nach dem Komma in der Variablen `avg_height`.\n",
|
||
|
|
"- Gegeben ist auch die Standardabweichung von 15cm, stelle die Normalverteilung mittels `norm.pdf` auf. Speichere den Wert in `norm_height` und finde einen geeigneten linespace zum plotten.\n",
|
||
|
|
"- Berechne folgend die Körpergröße unter die 80% aller Frauen (nach Datenset) fallen. Speichere den Wert in der Variablen `avg_percentile`.\n",
|
||
|
|
"- Plotte das Ergebnis. Orientiere dich gerne an dem Bienenbeispiel. Finde eine geeignete Darstellung. *Tipp: Da die Y-Achse in diesem Beispiel keinen Sinn ergibt kannst du sie einfach austellen mit `plt.yticks([])`*\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 87,
|
||
|
|
"id": "3983d224-e885-43bd-aadd-4e276a56a370",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": false,
|
||
|
|
"grade_id": "cell-048d8330d555432a",
|
||
|
|
"locked": true,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# Given\n",
|
||
|
|
"avg_height_per_woman = {\n",
|
||
|
|
" \"18 - 20\": 167.6,\n",
|
||
|
|
" \"20 - 25\": 167.7,\n",
|
||
|
|
" \"25 - 30\": 167.3,\n",
|
||
|
|
" \"30 - 35\": 167.2,\n",
|
||
|
|
" \"35 - 40\": 167.3,\n",
|
||
|
|
" \"40 - 45\": 167.5,\n",
|
||
|
|
" \"45 - 50\": 167.1,\n",
|
||
|
|
" \"50 - 55\": 167.1,\n",
|
||
|
|
" \"55 - 60\": 166.9,\n",
|
||
|
|
" \"60 - 65\": 165.4,\n",
|
||
|
|
" \"65 - 70\": 164.5,\n",
|
||
|
|
" \"70 - 75\": 163.9,\n",
|
||
|
|
" \"75+\": 162.8\n",
|
||
|
|
"}\n",
|
||
|
|
"\n",
|
||
|
|
"avg_height = None\n",
|
||
|
|
"norm_height = None\n",
|
||
|
|
"avg_percentile = None"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 138,
|
||
|
|
"id": "2c2e2cf6-c743-4cb0-a329-2240205fc7da",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-a59f2b3230aad3d6",
|
||
|
|
"locked": false,
|
||
|
|
"points": 3,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": true,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 900x600 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"# BEGIN SOLUTION\n",
|
||
|
|
"avg_height = np.round(np.mean(list(avg_height_per_woman.values())), decimals=1)\n",
|
||
|
|
"std_sigma = 15\n",
|
||
|
|
"\n",
|
||
|
|
"norm_x = np.linspace(120, 220, 1000)\n",
|
||
|
|
"norm_height = stats.norm(avg_height, std_sigma).pdf(norm_x)\n",
|
||
|
|
"\n",
|
||
|
|
"# Height of 80th percentile of woman heights\n",
|
||
|
|
"avg_percentile = stats.norm(avg_height, std_sigma).ppf(0.8)\n",
|
||
|
|
"\n",
|
||
|
|
"x_percentile = np.arange(norm_x[0], avg_percentile, 0.01)\n",
|
||
|
|
"y_percentile = stats.norm(avg_height, std_sigma).pdf(x_percentile)\n",
|
||
|
|
"\n",
|
||
|
|
"# Plot\n",
|
||
|
|
"fig, ax = plt.subplots(figsize=(9,6))\n",
|
||
|
|
"ax.plot(norm_x, norm_height, color='r')\n",
|
||
|
|
"\n",
|
||
|
|
"# filling under the curve\n",
|
||
|
|
"ax.fill_between(x_percentile, y_percentile, 0, alpha=.5, color='#fa0000')\n",
|
||
|
|
"\n",
|
||
|
|
"\n",
|
||
|
|
"# Set text\n",
|
||
|
|
"ax.text(0.4,0.18,\n",
|
||
|
|
" f\"80th percentile of Womens heigth\\n fall under {avg_percentile:.1f}cm\",\n",
|
||
|
|
" ha='center', va='center', transform=ax.transAxes,\n",
|
||
|
|
" bbox={'facecolor':'#fafafa','alpha':1,'edgecolor':'none','pad':1},\n",
|
||
|
|
" color='#de2e0b'\n",
|
||
|
|
" )\n",
|
||
|
|
"\n",
|
||
|
|
"# Show\n",
|
||
|
|
"plt.title(\"Woman Height Normal Distribution\")\n",
|
||
|
|
"plt.xlabel(\"Height\")\n",
|
||
|
|
"plt.yticks([]) # hide y\n",
|
||
|
|
"plt.show()\n",
|
||
|
|
"# END SOLUTION"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 150,
|
||
|
|
"id": "d9f8aeae-6b51-4645-b578-19693a07ece3",
|
||
|
|
"metadata": {
|
||
|
|
"nbgrader": {
|
||
|
|
"grade": true,
|
||
|
|
"grade_id": "cell-26f141bc8b12d7fe",
|
||
|
|
"locked": true,
|
||
|
|
"points": 3,
|
||
|
|
"schema_version": 3,
|
||
|
|
"solution": false,
|
||
|
|
"task": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# Hier werden ihre Lösungen getestet...\n",
|
||
|
|
"import math \n",
|
||
|
|
"\n",
|
||
|
|
"# Check if average height is close to real value\n",
|
||
|
|
"assert math.isclose(avg_height, 166.3, rel_tol=.2) # 1 Punkt\n",
|
||
|
|
"\n",
|
||
|
|
"# Check if norm height is close to real value\n",
|
||
|
|
"assert math.isclose(np.round(np.sum(norm_height), decimals=1), 10, rel_tol=.2) # 1 Punkt\n",
|
||
|
|
"\n",
|
||
|
|
"# Check if percentile is close to real value\n",
|
||
|
|
"assert math.isclose(avg_percentile, 179, rel_tol=.2) # 1 Punkt"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "f50b8883-e018-4a44-831a-1a3c14640955",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Probabillity Mass Function - Binomial Verteilung\n",
|
||
|
|
"\n",
|
||
|
|
"Im Gegensatz zur Normal Verteilung folgen Binomiale Verteilungen Diskreten Werten. Dies lässt sich am besten am Beispiel zweier unabhängiger Würfel zeigen.\n",
|
||
|
|
"\n",
|
||
|
|
"Wir wollen im folgenden also aufzeigen wie die Wahrscheinlichkeits Verteilung zweier 6 seitiger Würfel ist. Da wir die Augenzahl beider Bestimmen führen wir eine Addition aller möglichen Werte vor. Da uns die Auftrittswahrscheinlichkeit interessiert eignet sich ein dict zum speichern der Daten. Dabei ist der Schlüssel die Augenzahl und der Wert die Autrittsanzahl:"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 160,
|
||
|
|
"id": "7a58ad07-9593-4c58-9a86-23a002ef5e94",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"{2: 1, 3: 2, 4: 3, 5: 4, 6: 5, 7: 6, 8: 5, 9: 4, 10: 3, 11: 2, 12: 1}\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"# Two Dices\n",
|
||
|
|
"first_dice: np.array = np.arange(1,7)\n",
|
||
|
|
"second_dice: np.array = np.arange(1,7)\n",
|
||
|
|
"\n",
|
||
|
|
"# Creating a dict with all keys\n",
|
||
|
|
"dist: dict = {el: 0 for el in range(2,13)}\n",
|
||
|
|
"\n",
|
||
|
|
"# Summing all possible combinations and store them inside the dict\n",
|
||
|
|
"for el1 in first_dice:\n",
|
||
|
|
" for el2 in second_dice:\n",
|
||
|
|
" dice_roll: int = el1 + el2\n",
|
||
|
|
" dist[dice_roll] += 1\n",
|
||
|
|
"\n",
|
||
|
|
"# Print the result\n",
|
||
|
|
"print(dist)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "0b2ff2d3-e8b0-45e9-9429-8db1acc5e526",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"Wie wir erstmal sehen können folgen die Zahl einem Muster, dieses lässt sich mittels Balkendiagramm visualisieren:"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 176,
|
||
|
|
"id": "f7915dad-d12a-4db1-b691-3fd53ead4027",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.bar(dist.keys(), dist.values(), color='#F00a00')\n",
|
||
|
|
"plt.xticks(list(dist.keys()))\n",
|
||
|
|
"plt.title(\"Double Dice role distribution\")\n",
|
||
|
|
"plt.xlabel(\"Points rolled\")\n",
|
||
|
|
"plt.ylabel(\"Number of occurrences\")\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"id": "13e3406d-bb54-482c-a76c-a45a4c309a76",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"Selbiges nur in Prozent statt absolut"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 214,
|
||
|
|
"id": "db27df8d-7bc1-418b-997a-01684eb6fc1e",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"np.float64(nan)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 214,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"vals = np.arange(2,13)\n",
|
||
|
|
"mean, var = stats.binom.stats(13, 0.5)\n",
|
||
|
|
"dist = stats.binom.pmf(7, mean, var)\n",
|
||
|
|
"dist"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 198,
|
||
|
|
"id": "41b90981-ef18-40b4-bb03-9cd3407869b4",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.bar(np.arange(2,12),stats.binom.pmf(np.arange(2,12), 12, 0.5))\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 209,
|
||
|
|
"id": "1d3d7273-ed46-42e4-8ce6-cded64f81e5c",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"<BarContainer object of 6 artists>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 209,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 640x480 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.bar(np.arange(1,7),stats.binom.pmf(np.arange(1,7), 6, 0.5) * stats.binom.pmf(np.arange(1,7), 6, 0.5))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 203,
|
||
|
|
"id": "2285d290-73a2-4c2d-8542-46c6aea2c71b",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"array([0.00878906, 0.05493164, 0.09765625, 0.05493164, 0.00878906])"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 203,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"stats.binom.pmf(np.arange(1,6), 6, 0.5) * stats.binom.pmf(np.arange(1,6), 6, 0.5)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"id": "9b142059-c19b-49c4-bc4b-02ca875b1fbf",
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"kernelspec": {
|
||
|
|
"display_name": "Python 3 (ipykernel)",
|
||
|
|
"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": "3.12.7"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 5
|
||
|
|
}
|