Will random numbers still be random if I systematically delete every nth one?
If they were indistinguishable from to true random begin with, they will be indistinguishable from true random afterwards.
The reason is that any correlation or bias that exists among the remaining numbers would also constitute a correlation or bias among the complete set. Therefore if the complete set is good then the subset is good.
Of course, this would not necessarily be the case if you deleted the numbers selectively based on their value, rather than based solely on their position in the sequence.
Also, if the numbers are not good to begin with then they might conceivably be worse afterwards than before. For an extreme example, consider a sequence that consists of 9 zeros followed by the result of a coin toss, 9 zeros and another coin toss, etc. This data source has some entropy (1 bit per 10 values), but if you remove every 10th element then it has none (the remaining output is known in advance).
I am currently using numpy.random.random_sample to compute a large set of random numbers. If I delete, say, every 10th of these numbers, is the result still going to be as random as before? Or would I introduce some sort of skew by doing this?
EDIT: As pointed out this boils down to how good my RNG is. How can I find out if I can trust a RNG, or how would I spot a potential skew?