What does "fixed but random" mean exactly? I am studying econometrics and bumped into such thing as "fixed but random" variables. As far as I understood, these are the observations that will become constant values in the future, when they are observed. But until they are not, so while we are "theorising", they can be seen as random variables, e.g., they can be iid from each other, so have their own distribution.
That's how I understood the concept, at least. So, we know that they aren't fully random variables: we know that each of them is a separated number, but we don't know which number exactly, so it is yet random. A random observation, so to say. And it has a distribution. Or is it the underlying random variable that has the distribution?
Sorry, I think I got confused. Especially because different textbooks and professors explain it differently and use different notations. I would be more than grateful if you provide any explanation or at least links to proper literature.
Sorry if it's not the proper place, but I don't know where else to ask. When I try to google "fixed but random", it results in distinguishing between fixed and random effects of panel data.
Thank you in advance!
EDIT -------------
First of all, thank you so much for taking time to comment and answer me!

*

*About the term itself:

I have heard the "fixed but random" term from only one of my professors, and have never seen it anywhere else. I just thought that it is how these things are called among those who are deeply into econometrics or something. It is definitely not from Bayes statistic, as I haven't yet got that far.


*About what I actually do not understand

I will try to describe a more precise situation for which I thought the term "fixed but random" is used (now, thanks to you, I understand that I was wrong).
I will now be "quoting" the lectures of one of my professors. They assume the case of linear regression model and write it like this:
$Y = b_1X_1 + ... + b_nX_n + e$
Then they say that in terms of the sample this model corresponds to:
$y_i = x_i^T b +e_i$
i = 1, ..., n,
where x_i and b are vectors.
And then they state the assumptions for the model like this:
the process/sequence
$(y_i , x_i^T)$
i ∊ ℕ
is iid.
And this is where I get confused. As far as I understand, the random variables are those Y and X_1, ..., X_n of the initial model. And y_i and x_i are a single (i-th) observation of Y and a vector of (i-th) observations of X respectively. So, they are fixed. But here comes a question: how can observations be iid from each other if they are fixed, so they don't have their own distribution, they are just constants.
That's why I thought that such observations are called "fixed but random", because we consider them to be not yet observations (we look at the distribution from which they occur), but not random variables, too, since we know that they are supposed to be fixed numbers. Probably I am somewhere wrong here. I would be very grateful if you could provide the explanation. I hope I described the situation more clearly now.
Thank you!
EDIT 2: I tried to ask it as a separate question but it got closed with some links to questions like "what is a random variable?" I understand how rv's differ from non-random values. I wanted explanation for this specific setting and formulation. So I will leave the edition here. Maybe someone will answer.

"fixed but random" is not a common term with a clear consensus about it's meaning.
The occurance of the term in the English literature is not common and half the time it is part of the phrase "not fixed but random"

Note that 'fixed but random' is not a contradiction when 'fixed' and 'random' relate to different things. But which relations, that depends on the context.

*

*Searching for the term on Google scholar I see several cases where 'fixed' refers to the situation where an object of study is fixed. And the 'random' part refers to the situation where this fixed state has been generated random.
For instance here

We are in a typical situation of the quenched disorder [3,4] when the motion of particles in a fixed but random environment is considered. That is why inevitably we are
faced with an averaging procedure, which helps us to pass to the macroscopic transport equation. $$$$ We have a fixed realization $b(x)=b(x_n)=b_n$ of a random
process (well depths)  with the probability distribution $P(b)$



*A situation of 'fixed but random' could also be the situation with Bayesian statistics where we use a prior distributions to express the probability distribution of some value which in reality may be a fixed value.


*Another situation of 'fixed but random' could be in description of random number generators. These can come up with a fixed sequence every time, but the numbers have a random character.
So this combination 'fixed but random' may occur and the meaning depends on the context. What it means for your econometrics case is not clear (since it is broad). It requires the specific context in order to say anything more about it.
