The Inbox is an Inbox for quick captures.

If an outcome can be from sets \(A=m\) or \(B=n\) with no overlaps, where \(A \cap B = \emptyset\), then, the total number of outcomes are \(|A| + |B| = m+n\)

If there are overlap:

\begin{equation} N = |A|+|B| - |A \cap B| \end{equation}

\(n\) random random variables are IID if they are

1. independent
2. identically distributed (see below)

“identically distributed”

Consider \(n\) random variables:

• \(X_i\) all have the same PMF / PDF
• and therefore, all have the same expectation and variance

central limit theorem

when things are IID, you can use central limit theorem.

Here’s a list of all indexes:

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This should be reflected on a fancier way on my home page.

voltage across a inductor

\begin{equation} V = \epsilon = -L \dv{I}{t} \end{equation}

this is kind of a formulation of faraday’s law.

\begin{equation} I(t) = \frac{V_0}{R_1} (1-e^{\frac{-t}{\frac{L}{R}}}) \end{equation}

energy stored in an inductor

\begin{equation} E = \frac{1}{2} LI^{2} \end{equation}