I am not a mathematician, but I *think* the question can be solved without any training set if you know "how random" the random numbers are (i.e. what's the distribution)?

For instance, it's easy to see that if the numbers are evenly distributed between 0 and 1, for N random numbers N / 2 would be have the highest frequency, while 0 and N would have the lowest.

Sorry for derailing this thread if you've got good reason to need the training set - just a thought.