# Combination of distributions [reference request]

Consider a random variable $$X:\Omega \rightarrow E$$ that combines multiple distributions:

$$X(\omega)\sim\begin{cases} N(0,\sigma^2),\hspace{0.2cm} \text{if \omega =0}\\ \text{beta}(0,1), \hspace{0.2cm} \text{if \omega =1} \end{cases}$$

Is there a concept for a random variable that combines multiple probabilitiy distributions?

A good answer would be of the sort:

Yes these are called [something]-distributions, and are commonly used in sub-field x. A good reference for these is work y.

or

No, these are not useful because of [reasons], and have no formal treatment as far as I know