Random Variables (RV)

- A variable is
*random*if it can take some value with certain probability

A RV is *discrete* if it takes certain isolated values.

- the # of possible values can be finite or infinite
- example: the number of born boys

A RV is continuous if it can take all values from some interval

In Statistics and Data Analysis, there are different names for the same thing:

A distribution of an RV is a mapping from possible values of RV to probabilities

- it can be a table (for discrete RVs) or a function (for continuous RVs)
- the sum of all probabilities must be 1

A distribution of an RV can be specified by

Most important parameters for an RV $X$ are:

- $E[X]$ or sometimes $M[X]$ - Expected Value, the mean value
- $\text{Var}[X]$ - Variance, how the variable is "spread out", measured in (units of $X$)${}^2$
- $\text{sd}[X] = \sqrt{\text{Var}[X]}$ - Standard Deviation, also a measure of variance, but in the same units as $X$

- Гмурман В.Е., Теория вероятностей и математическая статистика -- 9-е издание. М.: Высш. шк., 2003.
- http://en.wikipedia.org/wiki/Probability_distribution