Random Variable

Random Variable

Random Variables (RV)

• A variable is ‘‘random’’ if it can take some value with certain probability

Types of Random Variables

Discrete Random Variables

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

Continuous Random Variables

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

Statistics

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

• Types of Variables
• Quantitative Variables
• Categorical Variables

Distributions

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

• Distribution Function
• Probability Density Function

Parameters

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 $X$

Sources

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