From 029b2427e379db3292e26441e0f0bc3e802338d9 Mon Sep 17 00:00:00 2001
From: Morten Hjorth-Jensen <morten.hjorth-jensen@fys.uio.no>
Date: Tue, 19 Sep 2023 11:49:04 +0200
Subject: [PATCH] small change

---
 .../2023/Project1/html/._Project1-bs000.html  |   4 +-
 .../2023/Project1/html/Project1-bs.html       |   4 +-
 doc/Projects/2023/Project1/html/Project1.html |   4 +-
 .../2023/Project1/ipynb/Project1.ipynb        | 104 +++++++++---------
 .../Project1/ipynb/ipynb-Project1-src.tar.gz  | Bin 193 -> 193 bytes
 doc/Projects/2023/Project1/pdf/Project1.p.tex |   4 +-
 doc/Projects/2023/Project1/pdf/Project1.pdf   | Bin 270582 -> 270659 bytes
 doc/Projects/2023/Project1/pdf/Project1.tex   |   4 +-
 .../Projects/2023/Project1/Project1.do.txt    |   4 +-
 9 files changed, 64 insertions(+), 64 deletions(-)

diff --git a/doc/Projects/2023/Project1/html/._Project1-bs000.html b/doc/Projects/2023/Project1/html/._Project1-bs000.html
index 24af4358b..905d9da71 100644
--- a/doc/Projects/2023/Project1/html/._Project1-bs000.html
+++ b/doc/Projects/2023/Project1/html/._Project1-bs000.html
@@ -499,10 +499,10 @@ $$
 
 <p>and </p>
 $$
-\mathrm{var}[\tilde{y}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2.
+\mathrm{var}[\tilde{y}]=\mathbb{E}\left[\left(\tilde{\boldsymbol{y}}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]\right)^2\right]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2.
 $$
 
-<p>The answer to this exercise should be included in the theory part of the report.  This exercise is also part of the weekly exercises of week 37.
+<p>The answer to this exercise should be included in the theory part of the report.  This exercise is also part of the weekly exercises of week 38.
 Explain what the terms mean and discuss their interpretations.
 </p>
 
diff --git a/doc/Projects/2023/Project1/html/Project1-bs.html b/doc/Projects/2023/Project1/html/Project1-bs.html
index 24af4358b..905d9da71 100644
--- a/doc/Projects/2023/Project1/html/Project1-bs.html
+++ b/doc/Projects/2023/Project1/html/Project1-bs.html
@@ -499,10 +499,10 @@ $$
 
 <p>and </p>
 $$
-\mathrm{var}[\tilde{y}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2.
+\mathrm{var}[\tilde{y}]=\mathbb{E}\left[\left(\tilde{\boldsymbol{y}}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]\right)^2\right]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2.
 $$
 
-<p>The answer to this exercise should be included in the theory part of the report.  This exercise is also part of the weekly exercises of week 37.
+<p>The answer to this exercise should be included in the theory part of the report.  This exercise is also part of the weekly exercises of week 38.
 Explain what the terms mean and discuss their interpretations.
 </p>
 
diff --git a/doc/Projects/2023/Project1/html/Project1.html b/doc/Projects/2023/Project1/html/Project1.html
index 41ec77b79..9e087eae6 100644
--- a/doc/Projects/2023/Project1/html/Project1.html
+++ b/doc/Projects/2023/Project1/html/Project1.html
@@ -535,10 +535,10 @@ $$
 
 <p>and </p>
 $$
-\mathrm{var}[\tilde{y}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2.
+\mathrm{var}[\tilde{y}]=\mathbb{E}\left[\left(\tilde{\boldsymbol{y}}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right]\right)^2\right]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2.
 $$
 
-<p>The answer to this exercise should be included in the theory part of the report.  This exercise is also part of the weekly exercises of week 37.
+<p>The answer to this exercise should be included in the theory part of the report.  This exercise is also part of the weekly exercises of week 38.
 Explain what the terms mean and discuss their interpretations.
 </p>
 
diff --git a/doc/Projects/2023/Project1/ipynb/Project1.ipynb b/doc/Projects/2023/Project1/ipynb/Project1.ipynb
index 467bad587..e28db853b 100644
--- a/doc/Projects/2023/Project1/ipynb/Project1.ipynb
+++ b/doc/Projects/2023/Project1/ipynb/Project1.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "7424fea1",
+   "id": "ee871b85",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c9ca1d90",
+   "id": "de647a13",
    "metadata": {
     "editable": true
    },
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e4164b6",
+   "id": "f0094ea8",
    "metadata": {
     "editable": true
    },
@@ -63,7 +63,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dd4dcdf5",
+   "id": "9d47e07f",
    "metadata": {
     "editable": true
    },
@@ -85,7 +85,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "71ddc478",
+   "id": "13b3c63c",
    "metadata": {
     "editable": true
    },
@@ -100,7 +100,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d4184afb",
+   "id": "588eb391",
    "metadata": {
     "editable": true
    },
@@ -133,7 +133,7 @@
   {
    "cell_type": "code",
    "execution_count": 1,
-   "id": "62880fe6",
+   "id": "2b565e88",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -185,7 +185,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f7e7c97",
+   "id": "5a80d8fa",
    "metadata": {
     "editable": true
    },
@@ -207,7 +207,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7377112f",
+   "id": "2b8a75d3",
    "metadata": {
     "editable": true
    },
@@ -220,7 +220,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "72f83fe7",
+   "id": "de8e68ca",
    "metadata": {
     "editable": true
    },
@@ -232,7 +232,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a3578ff",
+   "id": "70a2795e",
    "metadata": {
     "editable": true
    },
@@ -244,7 +244,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e0aef819",
+   "id": "07d74c94",
    "metadata": {
     "editable": true
    },
@@ -254,7 +254,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c7f751af",
+   "id": "cb7a1688",
    "metadata": {
     "editable": true
    },
@@ -266,7 +266,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c026a4bd",
+   "id": "0c273378",
    "metadata": {
     "editable": true
    },
@@ -295,7 +295,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2635bcbd",
+   "id": "b6aa07e9",
    "metadata": {
     "editable": true
    },
@@ -313,7 +313,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "92892df2",
+   "id": "4c297a7f",
    "metadata": {
     "editable": true
    },
@@ -330,7 +330,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "35987aab",
+   "id": "9b65abbd",
    "metadata": {
     "editable": true
    },
@@ -346,7 +346,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e61048c2",
+   "id": "9f2c97bc",
    "metadata": {
     "editable": true
    },
@@ -358,7 +358,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5ef456d4",
+   "id": "1390caea",
    "metadata": {
     "editable": true
    },
@@ -369,7 +369,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "52e6fbad",
+   "id": "757a87d4",
    "metadata": {
     "editable": true
    },
@@ -381,7 +381,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "db6028a0",
+   "id": "cf182a2a",
    "metadata": {
     "editable": true
    },
@@ -393,7 +393,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9477ad5e",
+   "id": "c7f15f3d",
    "metadata": {
     "editable": true
    },
@@ -405,7 +405,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8c2aeccd",
+   "id": "70c8c4e9",
    "metadata": {
     "editable": true
    },
@@ -416,7 +416,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a774b74",
+   "id": "3879a5b4",
    "metadata": {
     "editable": true
    },
@@ -428,7 +428,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "98fde9b7",
+   "id": "17191387",
    "metadata": {
     "editable": true
    },
@@ -441,7 +441,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87a4d11d",
+   "id": "a7e3a698",
    "metadata": {
     "editable": true
    },
@@ -453,7 +453,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b4844f1e",
+   "id": "93fc4a12",
    "metadata": {
     "editable": true
    },
@@ -463,7 +463,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f7662ade",
+   "id": "85d336ad",
    "metadata": {
     "editable": true
    },
@@ -475,7 +475,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d61362e",
+   "id": "869ed780",
    "metadata": {
     "editable": true
    },
@@ -486,7 +486,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "74bbb4ab",
+   "id": "88502fe8",
    "metadata": {
     "editable": true
    },
@@ -519,7 +519,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ac939724",
+   "id": "db4583da",
    "metadata": {
     "editable": true
    },
@@ -531,7 +531,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4066d012",
+   "id": "da3a0dfc",
    "metadata": {
     "editable": true
    },
@@ -550,7 +550,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e5c5ef4",
+   "id": "07b53a45",
    "metadata": {
     "editable": true
    },
@@ -562,7 +562,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "690337b9",
+   "id": "1d8bc8d4",
    "metadata": {
     "editable": true
    },
@@ -576,7 +576,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "92dabf3c",
+   "id": "7f06bfd3",
    "metadata": {
     "editable": true
    },
@@ -588,7 +588,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7da90966",
+   "id": "5624047e",
    "metadata": {
     "editable": true
    },
@@ -598,7 +598,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33a81d54",
+   "id": "1b26ef35",
    "metadata": {
     "editable": true
    },
@@ -610,7 +610,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "abb9bd28",
+   "id": "6319fcec",
    "metadata": {
     "editable": true
    },
@@ -620,24 +620,24 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5b4668fd",
+   "id": "2253bb98",
    "metadata": {
     "editable": true
    },
    "source": [
     "$$\n",
-    "\\mathrm{var}[\\tilde{y}]=\\frac{1}{n}\\sum_i(\\tilde{y}_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2.\n",
+    "\\mathrm{var}[\\tilde{y}]=\\mathbb{E}\\left[\\left(\\tilde{\\boldsymbol{y}}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]\\right)^2\\right]=\\frac{1}{n}\\sum_i(\\tilde{y}_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2.\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "b453f8fc",
+   "id": "d08baf03",
    "metadata": {
     "editable": true
    },
    "source": [
-    "The answer to this exercise should be included in the theory part of the report.  This exercise is also part of the weekly exercises of week 37.\n",
+    "The answer to this exercise should be included in the theory part of the report.  This exercise is also part of the weekly exercises of week 38.\n",
     "Explain what the terms mean and discuss their interpretations.\n",
     "\n",
     "Perform then a bias-variance analysis of the Franke function by\n",
@@ -651,7 +651,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6fe323b0",
+   "id": "d06c2f80",
    "metadata": {
     "editable": true
    },
@@ -676,7 +676,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5fd2f486",
+   "id": "2a957aee",
    "metadata": {
     "editable": true
    },
@@ -704,7 +704,7 @@
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "e88e39ea",
+   "id": "1c0d6323",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -716,7 +716,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "29817da1",
+   "id": "183f2666",
    "metadata": {
     "editable": true
    },
@@ -728,7 +728,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "560fc9f4",
+   "id": "3ccf3ab9",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -754,7 +754,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3fc05383",
+   "id": "cf6cdda9",
    "metadata": {
     "editable": true
    },
@@ -779,7 +779,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bb21261e",
+   "id": "f28a3bdf",
    "metadata": {
     "editable": true
    },
@@ -793,7 +793,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c5ab9dbf",
+   "id": "ed920879",
    "metadata": {
     "editable": true
    },
@@ -823,7 +823,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7d0dbb14",
+   "id": "f2bef519",
    "metadata": {
     "editable": true
    },
@@ -845,7 +845,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e301049d",
+   "id": "e1891d3f",
    "metadata": {
     "editable": true
    },
diff --git a/doc/Projects/2023/Project1/ipynb/ipynb-Project1-src.tar.gz b/doc/Projects/2023/Project1/ipynb/ipynb-Project1-src.tar.gz
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diff --git a/doc/Projects/2023/Project1/pdf/Project1.p.tex b/doc/Projects/2023/Project1/pdf/Project1.p.tex
index b886c97c4..c87a4528d 100644
--- a/doc/Projects/2023/Project1/pdf/Project1.p.tex
+++ b/doc/Projects/2023/Project1/pdf/Project1.p.tex
@@ -459,9 +459,9 @@ with
 \]
 and 
 \[
-\mathrm{var}[\tilde{y}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\bm{\tilde{y}}\right])^2.
+\mathrm{var}[\tilde{y}]=\mathbb{E}\left[\left(\tilde{\bm{y}}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2\right]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\bm{\tilde{y}}\right])^2.
 \]
-The answer to this exercise should be included in the theory part of the report.  This exercise is also part of the weekly exercises of week 37.
+The answer to this exercise should be included in the theory part of the report.  This exercise is also part of the weekly exercises of week 38.
 Explain what the terms mean and discuss their interpretations.
 
 Perform then a bias-variance analysis of the Franke function by
diff --git a/doc/Projects/2023/Project1/pdf/Project1.pdf b/doc/Projects/2023/Project1/pdf/Project1.pdf
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diff --git a/doc/Projects/2023/Project1/pdf/Project1.tex b/doc/Projects/2023/Project1/pdf/Project1.tex
index 0381df84e..2db7584c0 100644
--- a/doc/Projects/2023/Project1/pdf/Project1.tex
+++ b/doc/Projects/2023/Project1/pdf/Project1.tex
@@ -429,9 +429,9 @@ with
 \]
 and 
 \[
-\mathrm{var}[\tilde{y}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\bm{\tilde{y}}\right])^2.
+\mathrm{var}[\tilde{y}]=\mathbb{E}\left[\left(\tilde{\bm{y}}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2\right]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\bm{\tilde{y}}\right])^2.
 \]
-The answer to this exercise should be included in the theory part of the report.  This exercise is also part of the weekly exercises of week 37.
+The answer to this exercise should be included in the theory part of the report.  This exercise is also part of the weekly exercises of week 38.
 Explain what the terms mean and discuss their interpretations.
 
 Perform then a bias-variance analysis of the Franke function by
diff --git a/doc/src/Projects/2023/Project1/Project1.do.txt b/doc/src/Projects/2023/Project1/Project1.do.txt
index 8e58048f9..a1053a8f2 100644
--- a/doc/src/Projects/2023/Project1/Project1.do.txt
+++ b/doc/src/Projects/2023/Project1/Project1.do.txt
@@ -336,10 +336,10 @@ with
 and 
 !bt
 \[
-\mathrm{var}[\tilde{y}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\bm{\tilde{y}}\right])^2.
+\mathrm{var}[\tilde{y}]=\mathbb{E}\left[\left(\tilde{\bm{y}}-\mathbb{E}\left[\bm{\tilde{y}}\right]\right)^2\right]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\bm{\tilde{y}}\right])^2.
 \]
 !et
-The answer to this exercise should be included in the theory part of the report.  This exercise is also part of the weekly exercises of week 37.
+The answer to this exercise should be included in the theory part of the report.  This exercise is also part of the weekly exercises of week 38.
 Explain what the terms mean and discuss their interpretations.
 
 Perform then a bias-variance analysis of the Franke function by