Update ipynb

2023-06-16 12:31:43 +02:00 · 2023-06-16 12:31:43 +02:00 · 6b99136661
commit 6b99136661
parent 5a4bada9c5
2 changed files with 307 additions and 118 deletions
--- a/jupyter/The
+++ b/jupyter/The
@ -15142,7 +15142,8 @@ body[data-format='mobile'] .jp-OutputArea-child .jp-OutputArea-output {
 <img src="https://cdn-icons-png.flaticon.com/512/3997/3997691.png"/>
 <img src="https://upload.wikimedia.org/wikipedia/commons/thumb/5/53/Google_%22G%22_Logo.svg/2008px-Google_%22G%22_Logo.svg.png" />
 <img src="https://upload.wikimedia.org/wikipedia/commons/thumb/0/04/ChatGPT_logo.svg/1024px-ChatGPT_logo.svg.png" />
-<img src="https://static.vecteezy.com/system/resources/previews/023/636/525/original/3d-rendering-radiation-icons-sign-caution-danger-symbol-free-png.png" />
+<img src="https://www.artandstick.be/getsupercustomizedimage.php5?objid=289&colorid1=2&colorid2=4&colorid3=4&colorid4=4&colorid5=4&way=NORMAL&transparent=Y" />    
+<!-- <img src="https://static.vecteezy.com/system/resources/previews/023/636/525/original/3d-rendering- -radiation-icons-sign-caution-danger-symbol-free-png.png" /> -->
 <img src="https://thegraphicsfairy.com/wp-content/uploads/2016/07/Frog-Drawing-Green-3-GraphicsFairy.jpg" />
 </div>

@ -15156,7 +15157,7 @@ body[data-format='mobile'] .jp-OutputArea-child .jp-OutputArea-output {
 </div>
 <div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
 </div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput " data-mime-type="text/markdown">
-<h1 id="Fr%C3%B6sche,-Wetten,-Wetter-und-Wetterfr%C3%B6sche">Fr&#246;sche, Wetten, Wetter und Wetterfr&#246;sche<a class="anchor-link" href="#Fr%C3%B6sche,-Wetten,-Wetter-und-Wetterfr%C3%B6sche">&#182;</a></h1>
+<h1 id="Fr%C3%B6sche,-Wetter-und-Wetterfr%C3%B6sche">Fr&#246;sche, Wetter und Wetterfr&#246;sche<a class="anchor-link" href="#Fr%C3%B6sche,-Wetter-und-Wetterfr%C3%B6sche">&#182;</a></h1>
 </div>
 </div>
 </div>
@ -15217,12 +15218,12 @@ body[data-format='mobile'] .jp-OutputArea-child .jp-OutputArea-output {
 </div>
 </div>
 </div>
-</div><div id="cell-id=f8a3a4d9" class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs  ">
+</div><div id="cell-id=f8a3a4d9" class="jp-Cell jp-CodeCell jp-Notebook-cell   ">
 <div class="jp-Cell-inputWrapper">
 <div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
 </div>
 <div class="jp-InputArea jp-Cell-inputArea">
-<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[1]:</div>
+<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[11]:</div>
 <div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
     <div class="CodeMirror cm-s-jupyter">
 <div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
@ -15231,9 +15232,27 @@ body[data-format='mobile'] .jp-OutputArea-child .jp-OutputArea-output {

 <span class="n">p</span> <span class="o">=</span> <span class="mf">0.6</span> <span class="c1"># von l nach r</span>
 <span class="n">q</span> <span class="o">=</span> <span class="mf">0.2</span> <span class="c1"># von r nach l</span>
-<span class="n">N</span> <span class="o">=</span> <span class="mi">100_000</span> <span class="c1"># Simulationen</span>
+<span class="n">N</span> <span class="o">=</span> <span class="mi">1_000_000</span> <span class="c1"># Simulationen</span>

 <span class="c1"># Los geht&#39;s!</span>
+<span class="n">position</span> <span class="o">=</span>  <span class="mi">0</span> <span class="c1"># 0 : links, 1: rechts</span>
+<span class="n">counter</span> <span class="o">=</span> <span class="p">[</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span> <span class="p">]</span> <span class="c1"># anzahl besuche links/rechts</span>
+<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="p">):</span>
+    <span class="k">if</span> <span class="n">position</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+        <span class="k">if</span> <span class="n">uniform</span><span class="p">()</span> <span class="o">&lt;</span> <span class="n">p</span><span class="p">:</span> <span class="c1"># [0.0, 0.1, ..., 1.0] &lt; 0.6 ??</span>
+            <span class="n">counter</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
+            <span class="n">position</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">position</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">counter</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="k">if</span> <span class="n">uniform</span><span class="p">()</span> <span class="o">&lt;</span> <span class="n">q</span><span class="p">:</span> <span class="c1"># [0.0, 0.1, ..., 1.0] &lt; 0.2 ??</span>
+            <span class="n">counter</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
+            <span class="n">position</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">position</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">counter</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
+
+<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Der Frosch war </span><span class="si">{</span><span class="n">counter</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="si">}</span><span class="s2"> mal links und </span><span class="si">{</span><span class="n">counter</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="si">}</span><span class="s2"> mal rechts&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;In dezimal: </span><span class="si">{</span><span class="n">counter</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">/</span><span class="n">N</span><span class="si">:</span><span class="s2">.4f</span><span class="si">}</span><span class="s2"> und </span><span class="si">{</span><span class="n">counter</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">/</span><span class="n">N</span><span class="si">:</span><span class="s2">.4f</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
 </pre></div>

     </div>
@ -15241,6 +15260,28 @@ body[data-format='mobile'] .jp-OutputArea-child .jp-OutputArea-output {
 </div>
 </div>

+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+
+
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child">
+    
+    <div class="jp-OutputPrompt jp-OutputArea-prompt"></div>
+
+
+<div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain">
+<pre>Der Frosch war 250283 mal links und 749718 mal rechts
+In dezimal: 0.2503 und 0.7497
+</pre>
+</div>
+</div>
+
+</div>
+
+</div>
+
 </div><div id="cell-id=41017b8e" class="jp-Cell jp-CodeCell jp-Notebook-cell   ">
 <div class="jp-Cell-inputWrapper">
 <div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
@ -15288,8 +15329,8 @@ body[data-format='mobile'] .jp-OutputArea-child .jp-OutputArea-output {

 <div class="jp-RenderedText jp-OutputArea-output" data-mime-type="text/plain">
 <pre>100000/100000
-  0.2473 of the time at 0 (24728 total)
-  0.7527 of the time at 1 (75272 total)
+  0.2509 of the time at 0 (25094 total)
+  0.7491 of the time at 1 (74906 total)
 </pre>
 </div>
 </div>
@ -15697,7 +15738,7 @@ $$
 M = \frac{1}{10} \begin{pmatrix}6 &amp; 3 &amp; 1 \\ 4 &amp; 3 &amp; 3 \\ 1 &amp; 5 &amp; 4 \end{pmatrix}
 = \begin{pmatrix}0.6 &amp; 0.3 &amp; 0.1 \\ 0.4 &amp; 0.3 &amp; 0.3 \\ 0.1 &amp; 0.5 &amp; 0.4 \end{pmatrix}
 \end{align*}
-$$<p>Wenn es heute regnet $X_0 = \begin{pmatrix}1 &amp; 0 &amp; 0 \end{pmatrix}$, ist die Wettervorschau für morgen $X_0 \cdot M$, bzw für in einer Woche $X_0 \cdot M \cdot \dots M = X_0 \cdot M^{14}$.</p>
+$$<p>Wenn heute die Sonne scheint $X_0 = \begin{pmatrix}1 &amp; 0 &amp; 0 \end{pmatrix}$, ist die Wettervorschau für morgen $X_0 \cdot M$, bzw für in zwei Wochen $X_{14} = X_0 \cdot  M \cdot \dots M = X_0 \cdot M^{14}$.</p>

 </div>
 </div>
@ -15807,14 +15848,18 @@ $$
 <div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
 </div>
 <div class="jp-InputArea jp-Cell-inputArea">
-<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[9]:</div>
+<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[29]:</div>
 <div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
     <div class="CodeMirror cm-s-jupyter">
-<div class=" highlight hl-ipython3"><pre><span></span><span class="c1">#from sympy import symbols as S, Matrix as Mat</span>
-<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span>
+<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span>

-<span class="n">M</span> <span class="o">=</span> <span class="n">array</span><span class="p">([[</span><span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.4</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">]])</span>
-<span class="n">x0</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
+<span class="n">M</span> <span class="o">=</span> <span class="n">array</span><span class="p">([</span>
+    <span class="p">[</span><span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">],</span> 
+    <span class="p">[</span><span class="mf">0.4</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">,</span> <span class="mf">0.3</span><span class="p">],</span> 
+    <span class="p">[</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">]]</span>
+<span class="p">)</span>
+
+<span class="n">x0</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="o">/</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="o">/</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="o">/</span><span class="mi">3</span><span class="p">]</span> <span class="c1"># regen</span>
 <span class="n">x0</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span> <span class="o">@</span> <span class="n">M</span>
 </pre></div>

@ -15831,13 +15876,13 @@ $$
 <div class="jp-OutputArea jp-Cell-outputArea">
 <div class="jp-OutputArea-child jp-OutputArea-executeResult">
    
-    <div class="jp-OutputPrompt jp-OutputArea-prompt">Out[9]:</div>
+    <div class="jp-OutputPrompt jp-OutputArea-prompt">Out[29]:</div>




 <div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain">
-<pre>array([0.40909225, 0.3484844 , 0.24242335])</pre>
+<pre>array([0.40909064, 0.34848494, 0.24242442])</pre>
 </div>

 </div>
@ -15846,16 +15891,16 @@ $$

 </div>

-</div><div id="cell-id=ae437f47" class="jp-Cell jp-CodeCell jp-Notebook-cell jp-mod-noOutputs  ">
+</div><div id="cell-id=ae437f47" class="jp-Cell jp-CodeCell jp-Notebook-cell   ">
 <div class="jp-Cell-inputWrapper">
 <div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
 </div>
 <div class="jp-InputArea jp-Cell-inputArea">
-<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[&nbsp;]:</div>
+<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[34]:</div>
 <div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
     <div class="CodeMirror cm-s-jupyter">
 <div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">linalg</span>
-<span class="n">x0</span> <span class="o">@</span> <span class="n">linalg</span><span class="o">.</span><span class="n">matrix_power</span><span class="p">(</span><span class="n">M</span><span class="p">,</span> <span class="mi">14</span><span class="p">)</span>
+<span class="n">x0</span> <span class="o">@</span> <span class="n">linalg</span><span class="o">.</span><span class="n">matrix_power</span><span class="p">(</span><span class="n">M</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span> <span class="c1"># schnelles Exponenzieren</span>
 </pre></div>

     </div>
@ -15863,6 +15908,29 @@ $$
 </div>
 </div>

+<div class="jp-Cell-outputWrapper">
+<div class="jp-Collapser jp-OutputCollapser jp-Cell-outputCollapser">
+</div>
+
+
+<div class="jp-OutputArea jp-Cell-outputArea">
+<div class="jp-OutputArea-child jp-OutputArea-executeResult">
+    
+    <div class="jp-OutputPrompt jp-OutputArea-prompt">Out[34]:</div>
+
+
+
+
+<div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain">
+<pre>array([0.40909091, 0.34848485, 0.24242424])</pre>
+</div>
+
+</div>
+
+</div>
+
+</div>
+
 </div>
 <div id="cell-id=6efbd936" class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
 <div class="jp-Cell-inputWrapper">
@ -15892,7 +15960,7 @@ $$<p>aus. Hierbei ist $\lambda != 0$ eine Zahl, die man auch <em>Eigenwert</em>
 <div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
 </div>
 <div class="jp-InputArea jp-Cell-inputArea">
-<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[13]:</div>
+<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[5]:</div>
 <div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
     <div class="CodeMirror cm-s-jupyter">
 <div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># linalg.eig berechnet Rechts-Eigenvektoren von Matrizen, wir suchen allerdings Links-Eigenvektoren</span>
@ -15949,7 +16017,7 @@ $$<p>aus. Hierbei ist $\lambda != 0$ eine Zahl, die man auch <em>Eigenwert</em>
 <div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
 </div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput " data-mime-type="text/markdown">
 <h1 id="Fr%C3%B6sche-brauchen-Zufall">Fr&#246;sche brauchen Zufall<a class="anchor-link" href="#Fr%C3%B6sche-brauchen-Zufall">&#182;</a></h1><div class="alert alert-info">
-<p>Viele Leute werfen Münzen in den Teich der Frösche.
+<p>Viele Leute werfen <strong>faire</strong> Münzen in den Teich der Frösche.
 Wir sollen einen Frosch aussuchen, der der neue Schatzmeister werden soll. 
 Wie können wir aus den 7 Fröschen <strong>fair</strong> einen auswählen?</p>
 </div>
@ -15990,7 +16058,7 @@ Wie können wir aus den 7 Fröschen <strong>fair</strong> einen auswählen?</p>
 <div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
 </div>
 <div class="jp-InputArea jp-Cell-inputArea">
-<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[32]:</div>
+<div class="jp-InputPrompt jp-InputArea-prompt">In&nbsp;[45]:</div>
 <div class="jp-CodeMirrorEditor jp-Editor jp-InputArea-editor" data-type="inline">
     <div class="CodeMirror cm-s-jupyter">
 <div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span>
@ -16012,7 +16080,7 @@ Wie können wir aus den 7 Fröschen <strong>fair</strong> einen auswählen?</p>
 <span class="p">[</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">0.0</span> <span class="p">,</span> <span class="mf">1.0</span><span class="p">]</span>
 <span class="p">])</span>
 <span class="n">v</span> <span class="o">=</span> <span class="n">array</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span> <span class="p">])</span>
-<span class="n">v</span> <span class="o">@</span> <span class="n">M</span>
+<span class="n">v</span> <span class="o">@</span> <span class="n">linalg</span><span class="o">.</span><span class="n">matrix_power</span><span class="p">(</span><span class="n">M</span><span class="p">,</span> <span class="mi">3</span><span class="o">*</span><span class="mi">7</span><span class="p">)</span>
 </pre></div>

     </div>
@ -16028,14 +16096,16 @@ Wie können wir aus den 7 Fröschen <strong>fair</strong> einen auswählen?</p>
 <div class="jp-OutputArea jp-Cell-outputArea">
 <div class="jp-OutputArea-child jp-OutputArea-executeResult">
    
-    <div class="jp-OutputPrompt jp-OutputArea-prompt">Out[32]:</div>
+    <div class="jp-OutputPrompt jp-OutputArea-prompt">Out[45]:</div>




 <div class="jp-RenderedText jp-OutputArea-output jp-OutputArea-executeResult" data-mime-type="text/plain">
-<pre>array([0. , 0.5, 0.5, 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ,
-       0. ])</pre>
+<pre>array([4.76837158e-07, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
+       0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.42857075e-01,
+       1.42857075e-01, 1.42857075e-01, 1.42857075e-01, 1.42857075e-01,
+       1.42857075e-01, 1.42857075e-01])</pre>
 </div>

 </div>
@ -16053,8 +16123,9 @@ Wie können wir aus den 7 Fröschen <strong>fair</strong> einen auswählen?</p>
 </div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput " data-mime-type="text/markdown">
 <h1 id="Markovketten">Markovketten<a class="anchor-link" href="#Markovketten">&#182;</a></h1><p>Die Prozesse, die wir bisher gesehen haben lassen sich als <em>Markovketten</em> verstehen. Die Ketten, die wir betrachten teilen die folgenden Eigenschaften:</p>
 <ul>
-<li>Zeit vergeht für unsere Prozesse $X_1, X_2, \dots$ <strong>diskret</strong></li>
+<li>Zeit vergeht für unsere Prozesse $X_0, X_1, X_2, \dots$ <strong>diskret</strong></li>
 <li>Wir können die Übergangswahrscheinlichkeiten in einer $n \times n$ Matrix $M$ auflisten</li>
+<li>Markovketten sind gedächtnislos</li>
 </ul>
 <p>Außerdem ist $M$ eine <em>stochastische Matrix</em> und erfüllt</p>
 <ul>
@ -16062,6 +16133,81 @@ Wie können wir aus den 7 Fröschen <strong>fair</strong> einen auswählen?</p>
 <li>jede Zeile summiert sich zu $1$</li>
 </ul>

+</div>
+</div>
+</div>
+</div>
+<div id="cell-id=3ca2367b" class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput " data-mime-type="text/markdown">
+<h1 id="A:-A-simple-Language-Model">A: A simple Language Model<a class="anchor-link" href="#A:-A-simple-Language-Model">&#182;</a></h1>
+</div>
+</div>
+</div>
+</div>
+<div id="cell-id=9598a4eb" class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput " data-mime-type="text/markdown">
+<div class="alert alert-info">
+<p>Mit dem <code>hp.txt</code>, generiere Harry Potter fanfiction! Ein brandneues Universum an Unsinn erwartet dich!</p>
+</div>
+
+</div>
+</div>
+</div>
+</div>
+<div id="cell-id=5dd3d18c" class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput " data-mime-type="text/markdown">
+<h1 id="B:-Monopoly">B: Monopoly<a class="anchor-link" href="#B:-Monopoly">&#182;</a></h1>
+</div>
+</div>
+</div>
+</div>
+<div id="cell-id=e436130d" class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput " data-mime-type="text/markdown">
+<div class="alert alert-info">
+<p>Wo sollte ich in Monopoly versuchen meine Häuser zu bauen?</p>
+</div>
+
+</div>
+</div>
+</div>
+</div>
+<div id="cell-id=ea10341b" class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput " data-mime-type="text/markdown">
+<h1 id="C:-Pagerank">C: Pagerank<a class="anchor-link" href="#C:-Pagerank">&#182;</a></h1>
+</div>
+</div>
+</div>
+</div>
+<div id="cell-id=e2faef6b" class="jp-Cell jp-MarkdownCell jp-Notebook-cell">
+<div class="jp-Cell-inputWrapper">
+<div class="jp-Collapser jp-InputCollapser jp-Cell-inputCollapser">
+</div>
+<div class="jp-InputArea jp-Cell-inputArea"><div class="jp-InputPrompt jp-InputArea-prompt">
+</div><div class="jp-RenderedHTMLCommon jp-RenderedMarkdown jp-MarkdownOutput " data-mime-type="text/markdown">
+<div class="alert alert-info">
+<p>Crawle eine kleine Wiki, analysiere ihre Links und finde die <em>relevantesten</em> Seiten!</p>
+</div>
+
 </div>
 </div>
 </div>
--- a/jupyter/The
+++ b/jupyter/The