Dirac delta function random variable probability
An example of such distributions could be a mix of discrete and continuous distributions—for example, a random variable that is 0 with probability 1/2, and takes a random value from a normal distribution with probability 1/2. It can still be studied to some extent by considering it to have a PDF of 



(
δ
[
x
]
+
φ
(
x
)
)

/

2


{\displaystyle (\delta [x]+\varphi (x))/2}

, where 



δ
[
x
]


{\displaystyle \delta [x]}

 is the Dirac delta function.
