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:
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
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