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


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 $X$