41 lines
1.4 KiB
XML
41 lines
1.4 KiB
XML
<?xml version="1.0" encoding="UTF-8"?>
|
|
|
|
<section xml:id="notes-02-03">
|
|
<title>Tuesday, Feb 3</title>
|
|
|
|
<introduction>
|
|
<p>
|
|
This is an outline of the topics we covered in class.
|
|
These notes are <em>not</em> a substitute for your own note-taking.
|
|
I highly recommend that you take your own notes during class.
|
|
If you ever miss a class for any reason, reach out to another student in class to get a copy of their notes.
|
|
</p>
|
|
</introduction>
|
|
|
|
|
|
<subsection>
|
|
<title>Variance</title>
|
|
|
|
<p>
|
|
Question: How spread out are <m>X</m> values? One answer we might try is to measure the average distance from the average value:
|
|
<md>
|
|
<mrow> \E\left[|X - \E(X)|\right] </mrow>
|
|
</md>
|
|
To simplify notation, we'll write <m>\mu = \E(X)</m>.
|
|
Also, it's often usefull to square a term rather than take absolute value when we want to ensure a positive output, so we'll define...
|
|
</p>
|
|
|
|
<definition xml:id="def-variance">
|
|
<statement>
|
|
<p>
|
|
Let <m>X</m> be a random variable with <m>\E(X) = \mu</m>.
|
|
The <term>variance</term> of <m>X</m> is:
|
|
<md>
|
|
<mrow> \sigma^2 = \Var(x) = \E\left[ (X - \mu)^2\right] </mrow>
|
|
</md>
|
|
<m>\sigma = \sqrt{\Var(X)}</m> is called the <term>standard deviation</term>.
|
|
</p>
|
|
</statement>
|
|
</definition>
|
|
</subsection>
|
|
</section> |