are iid rvs with and

I need to make sure my understanding of this statement is correct.

If X is a rv, then it is a function defined over a sample space.

i = 1,2,3,....n constitute the number of trials of this rv.

are not random variables, but values which the random variable (a function) assumes.

So here's my confusion.

If is only a value, analogous to the range of a function, say, , what is the actual meaning of

and ? Is it just trying to imply that these values are all drawn from a RV whose parameters are and ?

Are they liberal with the semantics or is my understanding wrong?

Thanks for your time!