...
A RV X is defined by a function FX(x), called a cumulative distribution function (CDF) of X, which has the following properties:
Example
CDF of a RV:
Probability
For a RV X and any value a, FX(a) represents the probability that X is less than or equal to a, i.e.:
...
Probability Density Function
If a RV X is continuous, and there is a function fX(x), called the probability density function (PDF), such that:
then X is an absolutely continuous RV.
If X is differentiable at x, then:
The following are properties of a PDF:
Example
PDF of a continuous RV that is uniformly distributed on the interval [0,C]:
PDF of a continuous RV that is exponentially distributed with parameter α > 0:
