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Adding more exercises throughout

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andyeisenberg
2026-01-01 22:19:38 +00:00
parent ee9c9e7430
commit 3e039c853e
4 changed files with 806 additions and 41 deletions
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source/ch-Expected-Value.ptx
+74 -1
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@@ -1,7 +1,6 @@
<?xml version="1.0" encoding="UTF-8"?>
<!-- TODO make sure to include EV/Var of all standard distributions, perhaps include a table? -->
<chapter xml:id="ch-Expected-Value" xmlns:xi="http://www.w3.org/2001/XInclude">
<title>Expected Value and Variance</title>
@@ -880,6 +879,80 @@
<exercise>
<statement>
<p>
Calculate the covariance of <m>X</m> and <m>Y</m>:
</p>
<table>
<title></title>
<tabular halign="center">
<row header="yes" bottom="minor">
<cell right="minor"></cell>
<cell right="minor"><m>X = 1</m></cell>
<cell><m>X = 2</m></cell>
</row>
<row bottom="minor">
<cell right="minor"><m>Y = 0</m></cell>
<cell right="minor">0.12</cell>
<cell>0.24</cell>
</row>
<row>
<cell right="minor"><m>Y = 1</m></cell>
<cell right="minor">0.3</cell>
<cell>34</cell>
</row>
</tabular>
</table>
</statement>
</exercise>
<exercise>
<statement>
<p>
Calculate the covariance of <m>X</m> and <m>Y</m>:
</p>
<table>
<title></title>
<tabular halign="center">
<row header="yes" bottom="minor">
<cell right="minor"></cell>
<cell right="minor"><m>X = 0</m></cell>
<cell right="minor"><m>X = 1</m></cell>
<cell><m>X = 2</m></cell>
</row>
<row bottom="minor">
<cell right="minor"><m>Y = 0</m></cell>
<cell right="minor">0.08</cell>
<cell right="minor">0.16</cell>
<cell>0.1</cell>
</row>
<row>
<cell right="minor"><m>Y = 1</m></cell>
<cell right="minor">0.14</cell>
<cell right="minor">0.2</cell>
<cell>0.32</cell>
</row>
</tabular>
</table>
</statement>
</exercise>
<exercise>
<statement>
<p>
Suppose we roll a fair, 4-sided die two times.
Let <m>X</m> be the sum of the rolls, and let <m>Y</m> be the product of the rolls.
Find the covariance of <m>X</m> and <m>Y</m>.
</p>
<p>
[Note: Somewhat tedious.]
</p>
</statement>
</exercise>