When was a random variable first called a "random variable"? And why is it called as such? From measure theoretic foundations, it is clear that a random variable is neither random nor a variable. It is a deterministic function developed as follows:
Construct probability space: $(\Omega, \Sigma, \mathbb{P})$. Construct a measurable space: $(E, \mathcal{E})$. Then define random variable $X: \Omega \rightarrow E$, so that $X$ is a deterministic function parameterized as $X(\omega\in\Omega)$.
It is thus clearly a rather deterministic (non-random) function.
I'm thus curious as to its first official labelling as being a random variable. Is there a source or person who coined the term, and who also clearly justified as to why it should be thought as such?

As to who coined the term, I suggest checking out the two below posts:
https://hsm.stackexchange.com/questions/9716/who-coined-the-term-random-variable
https://hsm.stackexchange.com/questions/2223/who-introduced-random-variables-into-probability
And a helpful page on getting around the precise meaning of "Random":
https://towardsdatascience.com/but-what-is-a-random-variable-4265d84cb7e5

You see, the events corresponding to your experiment have inherent uncertainty (randomness) associated with it i.e. your two coin toss in above experiment could be HH or HT or TT or TH. You then use probability theory to quantify the uncertainty corresponding to these events. I appreciate that at the end of the day it is simply semantics but I really liked the word uncertainty as it helps me not bring in my understanding of randomness from other disciplines. This also means that Random Variables in statistics could have been called Uncertain Variables. But they are not called so :( ….. the literature consistently calls them Random Variable so if it helps, you could (as I often) do the translation in your mind to Uncertain Variables.

