Expressing a When statement in Elegant Mathematics

Question

I would like to elegantly describe the sentence below using mathematical notations.

In the case when distance $z$ between $x$ and $y$ follows a uniform distribution such that $z$ satisfies $[x, y]$ $(0\leq x< y)$, parameter $q$ can be obtained using Equation 1. Otherwise it is as given in Equation 2

$q = (e^-z) x^2 + y^2 $ ---------(1)

$q = \sqrt\frac{1}{2}z$ ---------(2)

How best could this be described?

Note: The parameter $q$ does not represent any unique mathematical expression I know in literature. I have included it to complete a framework for the question

Answer 1

Use definition by cases :

$\begin{equation*} q = \begin{cases} (e^{-z}) x^2 + y^2 & \text {when...}\\ \sqrt\frac{1}{2}z & \text{otherwise} \end{cases} \end{equation*}$