Continuous Random Variable

probability-theory

Definition

Continuous Random Variable

A random variable is called continuous if the image is uncountable.

Continuous Random Variable

A random variable is called continuous if there exists a function exists, such that:

Then, is called the probability density function of .

Properties:

• The density is non-negative, that is .
  
• The density integrates to 1, i.e.:

Note that the density is not a probability as the density can take values bigger than .