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Exercise24.3.html
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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN"
"HTMLFiles/xhtml-math11-f.dtd">
<!-- Created with the Wolfram Language : www.wolfram.com -->
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<title>
Exercise24.3
</title>
<link href="HTMLFiles/Exercise24.3.css" rel="stylesheet" type="text/css" />
</head>
<body>
<p class="Chapter">
Some setting
</p>
<p class="Subchapter">
Data
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_1.png" alt="Exercise24.3_1.png" width="408" height="13" style="vertical-align:middle" />
</p>
<p class="Output">
<img src="HTMLFiles/Exercise24.3_2.png" alt="Exercise24.3_2.png" width="376" height="13" style="vertical-align:middle" />
</p>
<p class="Subchapter">
Sample mean
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_3.png" alt="Exercise24.3_3.png" width="66" height="13" style="vertical-align:middle" />
</p>
<p class="Output">
<img src="HTMLFiles/Exercise24.3_4.png" alt="Exercise24.3_4.png" width="55" height="13" style="vertical-align:middle" />
</p>
<p class="Subchapter">
Normalizing constant
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_5.png" alt="Exercise24.3_5.png" width="160" height="37" style="vertical-align:middle" />
</p>
<p class="Output">
<img src="HTMLFiles/Exercise24.3_6.png" alt="Exercise24.3_6.png" width="310" height="65" style="vertical-align:middle" />
</p>
<p class="Chapter">
Posterior distribution function w.o. normalizing constant
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_7.png" alt="Exercise24.3_7.png" width="192" height="37" style="vertical-align:middle" />
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_8.png" alt="Exercise24.3_8.png" width="704" height="224" style="vertical-align:middle" />
</p>
<p class="Output">
<img src="HTMLFiles/Exercise24.3_9.png" alt="Exercise24.3_9.png" width="633" height="162" style="vertical-align:middle" />
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_10.png" alt="Exercise24.3_10.png" width="448" height="37" style="vertical-align:middle" />
</p>
<p class="Subchapter">
Define function for posterior distribution of one data
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_11.png" alt="Exercise24.3_11.png" width="86" height="13" style="vertical-align:middle" />
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_12.png" alt="Exercise24.3_12.png" width="696" height="181" style="vertical-align:middle" />
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_13.png" alt="Exercise24.3_13.png" width="635" height="34" style="vertical-align:middle" />
</p>
<p class="Output">
<img src="HTMLFiles/Exercise24.3_14.png" alt="Exercise24.3_14.png" width="55" height="13" style="vertical-align:middle" />
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_15.png" alt="Exercise24.3_15.png" width="231" height="37" style="vertical-align:middle" />
</p>
<p class="Output">
<img src="HTMLFiles/Exercise24.3_16.png" alt="Exercise24.3_16.png" width="136" height="48" style="vertical-align:middle" />
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_17.png" alt="Exercise24.3_17.png" width="109" height="32" style="vertical-align:middle" />
</p>
<p class="Output">
<img src="HTMLFiles/Exercise24.3_18.png" alt="Exercise24.3_18.png" width="189" height="38" style="vertical-align:middle" />
</p>
<p class="Chapter">
Plot
</p>
<p class="Subchapter">
Parameters
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_19.png" alt="Exercise24.3_19.png" width="84" height="13" style="vertical-align:middle" />
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_20.png" alt="Exercise24.3_20.png" width="226" height="13" style="vertical-align:middle" />
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_21.png" alt="Exercise24.3_21.png" width="4" height="13" style="vertical-align:middle" />
</p>
<p class="Subchapter">
Posterior P(μ|x) for one datum from Xn = -10
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_22.png" alt="Exercise24.3_22.png" width="214" height="13" style="vertical-align:middle" />
</p>
<p class="Output">
<img src="HTMLFiles/Exercise24.3_23.gif" alt="Exercise24.3_23.gif" width="360" height="230" style="vertical-align:middle" />
</p>
<p class="Subchapter">
Posterior P(μ|x) for one datum from Xn = -27
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_24.png" alt="Exercise24.3_24.png" width="215" height="13" style="vertical-align:middle" />
</p>
<p class="Output">
<img src="HTMLFiles/Exercise24.3_25.gif" alt="Exercise24.3_25.gif" width="360" height="227" style="vertical-align:middle" />
</p>
<p class="Subchapter">
Posterior P(μ|x) for all 7 data
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_26.png" alt="Exercise24.3_26.png" width="581" height="31" style="vertical-align:middle" />
</p>
<p class="Output">
<img src="HTMLFiles/Exercise24.3_27.gif" alt="Exercise24.3_27.gif" width="360" height="227" style="vertical-align:middle" />
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_28.png" alt="Exercise24.3_28.png" width="505" height="31" style="vertical-align:middle" />
</p>
<p class="Output">
<img src="HTMLFiles/Exercise24.3_29.gif" alt="Graphics:None" width="360" height="238" style="vertical-align:middle" />
</p>
<p class="Subchapter">
check a small bump around μ=-27
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_30.png" alt="Exercise24.3_30.png" width="581" height="31" style="vertical-align:middle" />
</p>
<p class="Output">
<img src="HTMLFiles/Exercise24.3_31.gif" alt="Exercise24.3_31.gif" width="360" height="220" style="vertical-align:middle" />
</p>
<p class="Input">
<img src="HTMLFiles/Exercise24.3_32.png" alt="Exercise24.3_32.png" width="505" height="31" style="vertical-align:middle" />
</p>
<p class="Output">
<img src="HTMLFiles/Exercise24.3_33.gif" alt="Graphics:None" width="360" height="231" style="vertical-align:middle" />
</p>
<div style="font-family:Helvetica; font-size:11px; width:100%; border:1px none #999999; border-top-style:solid; padding-top:2px; margin-top:20px;">
<a href="http://www.wolfram.com/language/" style="color:#000; text-decoration:none;">
<span style="color:#555555">Created with the Wolfram Language</span>
</a>
</div>
</body>
</html>