I have an equation,
$y = mx + n{\left| x \right|^2} + q{\left| x \right|^2}x + z$
Where, $m,n,q$ are deterministic complex number, $z$ is a complex Gaussian random variable with mean $\mu $ and variance $\sigma _z^2$, and $x$ is a random variable.
Now if I condition $y$ for a given $x$, the mean of $y$,
$E\left[ y \right] = mx + n{\left| x \right|^2} + q{\left| x \right|^2}x + \mu $
${\mathop{\rm var}} (y) = {m^2}{\left| x \right|^2} + {n^2}{\left| x \right|^4} + {q^2}{\left| x \right|^6} + \sigma _z^2$
Now how should I write, $p(y\mid x)$ (I am not sure if I am on the right track)?