Regarding question What is a realization of random variable? and similarly Probability: are realizations of random variables what is actually observed?:
I have a random variable $X$, such that $X$ is in the space $(\Omega,F,P)$, that is $X: (\Omega,F) \to (\mathbb R,B(\mathbb R))$.
A realization of $X$ is of the form $X(\omega)$, and an observed realization of $X$ is of the form $X(\omega_1)$, where the event $\omega_1$ happened and the value of $X(\omega_1)$ is (for simplicity) known and a real value, e.g., $X(ω_1 = \{\text{HEADS}\}) = 1$.
My question is, although somewhat strange: Is the OBSERVED REALIZATION, where both the event is known and the value for X for that event a random variable? I initially thought not, as it is neither a variable (its a value) nor random (it has been observed and therefore history in hindsight is deterministic).
Any insights or references?