Sets

Definition
A set is a collection of explicitly-defined distinct elements.
 

Elements of a Set
If 2, 4, 6, 8 are elements of A, we can then write

$A = \{0, ~ 2, ~ 4, ~ 6, ~ 8\}$

or it can be written using the set-builder notation

$A = \{x ~ : ~ x \text{ is an even digit} \}$

read as "A is the set of all x such that x is an even digit".
 

Counting Techniques

Fundamental Principle of Counting
If event E1 can have n1 different outcomes, event E2 can have n2 different outcomes, ..., and event Em can have nm different outcomes, then it follows that the number of possible outcomes in which composite events E1, E2, ..., Em can have is

n1 × n2 × ... × nm

We call this The Multiplication Principle.
 

Probability and Statistics

Mean
$\bar{x} = \dfrac{\Sigma x}{n}$   or   $\bar{x} = \dfrac{\Sigma xf}{\Sigma f}$
 

Variance
$\sigma^2 = \sum \dfrac{(x - \bar{x})^2}{n}$   or   $\sigma^2 = \dfrac{\Sigma (x - \bar{x})^2 f}{\Sigma f}$
 

Permutation
$^{n}P_k = \dfrac{n!}{(n - k)!}$
 

Combination
$\displaystyle ^{n}C_k = \binom{n}{k} = \dfrac{n!}{k! \, (n - k)!}$
 

Binomial Distribution
$P(x) = {^{n}C}_x \, p^x q^{n - x}$