correcting minor typos

doc/LectureNotes/_build/html/_sources/exercisesweek38.ipynb

@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "d8f7704f",
+   "id": "ce05d309",
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@@ -14,7 +14,7 @@
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   {
    "cell_type": "markdown",
-   "id": "9e388b87",
+   "id": "5b7c1442",
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@@ -27,7 +27,7 @@
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   {
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+   "id": "02e09b06",
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@@ -45,7 +45,7 @@
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@@ -57,7 +57,7 @@
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@@ -76,7 +76,7 @@
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@@ -88,7 +88,7 @@
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@@ -102,19 +102,19 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d65d4905",
+   "id": "25391aba",
    "metadata": {
     "editable": true
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    "source": [
     "$$\n",
-    "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathrm{Bias}[y]+\\mathrm{var}[\\tilde{y}]+\\sigma^2,\n",
+    "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathrm{Bias}[\\tilde{y}]+\\mathrm{var}[\\tilde{y}]+\\sigma^2,\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "d102dec2",
+   "id": "b6e8652c",
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@@ -124,19 +124,19 @@
   },
   {
    "cell_type": "markdown",
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+   "id": "77755270",
    "metadata": {
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    "source": [
     "$$\n",
-    "\\mathrm{Bias}[y]=\\mathbb{E}\\left[\\left(\\boldsymbol{y}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]\\right)^2\\right],\n",
+    "\\mathrm{Bias}[\\tilde{y}]=\\mathbb{E}\\left[\\left(\\boldsymbol{y}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]\\right)^2\\right],\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "fee09cce",
+   "id": "fa94db90",
    "metadata": {
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@@ -146,7 +146,7 @@
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@@ -158,7 +158,7 @@
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+   "id": "2dcb3e9a",
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doc/LectureNotes/_build/html/_sources/project1.ipynb

@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "ee871b85",
+   "id": "f8900c95",
    "metadata": {
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@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
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+   "id": "e1595afd",
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@@ -27,7 +27,7 @@
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@@ -63,7 +63,7 @@
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@@ -85,7 +85,7 @@
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@@ -100,7 +100,7 @@
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@@ -133,7 +133,7 @@
   {
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@@ -185,7 +185,7 @@
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@@ -207,7 +207,7 @@
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@@ -220,7 +220,7 @@
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@@ -232,7 +232,7 @@
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@@ -244,7 +244,7 @@
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@@ -254,7 +254,7 @@
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@@ -266,7 +266,7 @@
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@@ -295,7 +295,7 @@
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@@ -313,7 +313,7 @@
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@@ -330,7 +330,7 @@
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@@ -346,7 +346,7 @@
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@@ -358,7 +358,7 @@
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@@ -369,7 +369,7 @@
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@@ -381,7 +381,7 @@
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@@ -393,7 +393,7 @@
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@@ -405,7 +405,7 @@
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@@ -416,7 +416,7 @@
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@@ -428,7 +428,7 @@
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@@ -441,7 +441,7 @@
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@@ -453,7 +453,7 @@
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@@ -463,7 +463,7 @@
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@@ -475,7 +475,7 @@
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@@ -486,7 +486,7 @@
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@@ -519,7 +519,7 @@
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@@ -531,7 +531,7 @@
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@@ -550,7 +550,7 @@
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@@ -562,7 +562,7 @@
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@@ -576,19 +576,19 @@
   },
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-   "id": "7f06bfd3",
+   "id": "10d717b5",
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    "source": [
     "$$\n",
-    "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathrm{Bias}[y]+\\mathrm{var}[\\tilde{y}]+\\sigma^2,\n",
+    "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathrm{Bias}[\\tilde{y}]+\\mathrm{var}[\\tilde{y}]+\\sigma^2,\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "5624047e",
+   "id": "5858f4a4",
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@@ -598,19 +598,19 @@
   },
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-   "id": "1b26ef35",
+   "id": "c3b75de4",
    "metadata": {
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    "source": [
     "$$\n",
-    "\\mathrm{Bias}[y]=\\mathbb{E}\\left[\\left(\\boldsymbol{y}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]\\right)^2\\right],\n",
+    "\\mathrm{Bias}[\\tilde{y}]=\\mathbb{E}\\left[\\left(\\boldsymbol{y}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]\\right)^2\\right],\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "6319fcec",
+   "id": "b8cc130e",
    "metadata": {
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@@ -620,7 +620,7 @@
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@@ -632,7 +632,7 @@
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@@ -651,7 +651,7 @@
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-   "id": "d06c2f80",
+   "id": "4b962286",
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@@ -676,7 +676,7 @@
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+   "id": "8a4f9316",
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@@ -704,7 +704,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "1c0d6323",
+   "id": "96232c73",
    "metadata": {
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     "editable": true
@@ -716,7 +716,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "183f2666",
+   "id": "67545b6f",
    "metadata": {
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@@ -728,7 +728,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "3ccf3ab9",
+   "id": "bad8a459",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -754,7 +754,7 @@
   },
   {
    "cell_type": "markdown",
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+   "id": "1e6a8f3f",
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@@ -779,7 +779,7 @@
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   {
    "cell_type": "markdown",
-   "id": "f28a3bdf",
+   "id": "3e942cfc",
    "metadata": {
     "editable": true
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@@ -793,7 +793,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ed920879",
+   "id": "5451b425",
    "metadata": {
     "editable": true
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@@ -823,7 +823,7 @@
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   {
    "cell_type": "markdown",
-   "id": "f2bef519",
+   "id": "b0aabc96",
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@@ -845,7 +845,7 @@
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   {
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-   "id": "e1891d3f",
+   "id": "a6299b8f",
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doc/LectureNotes/_build/html/exercisesweek38.html

@@ -455,12 +455,12 @@ term which measures the deviation from the true data and the mean value of the m
 That is, show that</p>
 <div class="math notranslate nohighlight">
 \[
-\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathrm{Bias}[y]+\mathrm{var}[\tilde{y}]+\sigma^2,
+\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathrm{Bias}[\tilde{y}]+\mathrm{var}[\tilde{y}]+\sigma^2,
 \]</div>
 <p>with</p>
 <div class="math notranslate nohighlight">
 \[
-\mathrm{Bias}[y]=\mathbb{E}\left[\left(\boldsymbol{y}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]\right)^2\right],
+\mathrm{Bias}[\tilde{y}]=\mathbb{E}\left[\left(\boldsymbol{y}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]\right)^2\right],
 \]</div>
 <p>and</p>
 <div class="math notranslate nohighlight">

doc/LectureNotes/_build/html/project1.html

@@ -659,7 +659,7 @@ which polynomial fits the data best.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_21682/39730396.py:11: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
+<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22981/39730396.py:11: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
   ax = fig.gca(projection=&#39;3d&#39;)
 </pre></div>
 </div>
@@ -815,12 +815,12 @@ term which measures the deviation from the true data and the mean value of the m
 That is, show that</p>
 <div class="math notranslate nohighlight">
 \[
-\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathrm{Bias}[y]+\mathrm{var}[\tilde{y}]+\sigma^2,
+\mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathrm{Bias}[\tilde{y}]+\mathrm{var}[\tilde{y}]+\sigma^2,
 \]</div>
 <p>with</p>
 <div class="math notranslate nohighlight">
 \[
-\mathrm{Bias}[y]=\mathbb{E}\left[\left(\boldsymbol{y}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]\right)^2\right],
+\mathrm{Bias}[\tilde{y}]=\mathbb{E}\left[\left(\boldsymbol{y}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]\right)^2\right],
 \]</div>
 <p>and</p>
 <div class="math notranslate nohighlight">