Definition 90.
Let \(X\) be a random variable with \(\E(X) = \mu\text{.}\) The variance of \(X\) is:
\begin{gather*}
\sigma^2 = \Var(x) = \E\left[ (X - \mu)^2\right]
\end{gather*}
\(\sigma = \sqrt{\Var(X)}\) is called the standard deviation.
Section Tuesday, Feb 3
This is an outline of the topics we covered in class. These notes are not 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.
Subsection Variance
Question: How spread out are \(X\) values? One answer we might try is to measure the average distance from the average value:
\begin{gather*}
\E\left[|X - \E(X)|\right]
\end{gather*}
To simplify notation, we’ll write \(\mu = \E(X)\text{.}\) 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...
