absolutely continuous probability density function probability distribution random variable probability
The random variable 



X


{\displaystyle X}

 is said to have a continuous probability distribution if the corresponding CDF 



F


{\displaystyle F}

 is continuous. If 



F



{\displaystyle F\,}

 is absolutely continuous, i.e., its derivative exists and integrating the derivative gives us the CDF back again, then the random variable X is said to have a probability density function (PDF) or simply density 



f
(
x
)
=



d
F
(
x
)


d
x




.


{\displaystyle f(x)={\frac {dF(x)}{dx}}\,.}


