I am new to algeba and I cannot manage to find how to write the algebraic equation to explain that I randomly sample data contained in vectors without replacement.
I have e.g. vectors and
:
Both of length, say >1000.
How to write in an algebraic form that I randomly sample n (say n = 20 ; with n < length( and
) observations without replacement in these vectors (or just in one of them)?
Thanks for your help !
After gathering more information, I am afraid that there is in fact no algebraic expression to formulate random sampling in a population without replacement.
If I make no mistakes, the only way to express it is from the probability of an element to be selected.
So, given N the population size (e.g. of
) and n the sample size (with n < N), we can express:
with "P(e)")
the probability that element e is selected.
And we can add that the probability of vector S of size n is:
Am I right ?