Reference Card

1 Probability and Related Topics:

Notation

$O_i$ denotes sample point

$i$ .

$\mathcal{S}$ denotes the sample space.

$P\{O_{i}\}$ denotes the probability of

$O_i$ .

$f(x)$ denotes the probability that the random variable

$X$ takes on the value

$x$ .

$E(X)$ denotes the expected value of the random variable

$X$ .

$P(A)$ denotes the probability of event

$A$ .

$P(A|B)$ denotes the conditional probability of event

$A$ given event

$B$ .

$\lambda$ denotes the arrival rate.

$\mu$ denotes the service rate.

Important Facts/Results

$P(A \mbox{ or } B \mbox{ or both}) = P(A) + P(B) - P(A \mbox{ and } B)$

$P(A \mbox{ and } B) = P(A|B) \cdot P(B)$

Assuming certain assumptions are satisfied, the expected size of a queueing system is given by $\lambda / (\mu - \lambda)$ .

Assuming certain assumptions are satisfied, the expected time in a queueing system is given by $1 / (\mu - \lambda)$ .

2 File Sharing and Related Topics:

Notation

$N$ denotes the number of machines that want the file

$F$ denotes the size of the file (in bits)

$u_S$ denotes the source's upload rate

$u_i$ denotes the upload rate of machine

$i$

$d_i$ denotes the download rate of machine

$i$

$d_{\mbox{min}} = \min\{d_1, d_2, \ldots, d_N\}$

$D$ denotes the total time

Important Facts/Results

$D_{\text{Clint-Server}} = \max \left\{ \frac{NF}{u_S}, \frac{F}{d_{\mbox{min}}} \right\}$

$D_{\text{Peer-to-Peer}} \approx \max \left\{ \frac{F}{u_S}, \frac{F}{d_{\mbox{min}}}, \frac{NF}{u_\mbox{total}} \right\}$

3 Some HTML Elements:

The entire document is contained between an <html> tag and an </html> tag.

Metadata (i.e., data about the document) is contained between optional <head> and </head> tags.

The main part of the document is contained between a <body> tag and a </body> tag.

Paragraphs are contained between <p> and </p> tags. Paragraphs can contain text and other elements (e.g., images and links).

Images are specified using <img/> tags. They have a src attribute that contains the URL of the image file. The value of the src attribute follows the = character and is in quotes (e.g., <img src="DukeDog.png" />).

Links (or anchors) are specified using <a> and </a> tags. The URL of the link (i.e., the file to retrieve when the link is clicked) is specified with the href attribute. The value of the href follows the = character and is in quotes. The text of the link (i.e., the text that the user can click on to retrieve the URL) is contained between the <a> and </a> tags (e.g., <a href="http://www.cs.jmu.edu/index.html">JMU CS<a>).