# Introduction; Review of Random Variables

Probability :: Set Theory :: Definition :: Conditional :: Random :: Distribution :: R.V.S.

## Distribution functions

The
**
cumulative distribution function
**
(cdf) of an r.v.
is
defined for each
as

Properties of cdf:

- is non-decreasing: If then .
- is right-continuous: .

These four properties completely characterize the family of cdfs on the real line. Any function which satisfies these has a corresponding probability distribution.

- For : .
- . Thus, if is continuous at , .

Thus determines a unique probability distribution on , so and are uniquely related.