Question

Given:

• a sequence of random numbers
• X clients select Y numbers from the sequence, forming their own sub-sequences
• the rules governing the selection process is not known

Is there a mathematical property that guarantees that each client will end up with a random sequence of numbers? That is, is a subset of a random sequence also guaranteed to be random regardless of the selection process?

UPDATE: I was trying to establish if I could use a single random-number generator to dish out values to multiple clients: Do stateless random number generators exist? — That is, clients choose elements from the sequence without replacement. That being said, I was wondering about the general case as well (when the selection rules are not known).

Answer 1

The word ‘random’ in ‘a sequence of random numbers’ is generally construed to mean that there is no additional information about any element of the sequence from looking at any other elements of the sequence. (i.e. the a priori and a posteriori probability distributions of element X_i are the same before and after studying any of the other elements.)

As long as none of the numbers are used by more than one client, you should be fine. (edit: and as others have mentioned, you can’t decide to accept one of the elements after you look at its value.)