without knowing anything about the background of the function and what it is used for, I give it the max. possible domain (the set or interval of all possible input values).
and so,
Defined for all m >= 0 and n >= 0.
there is no information provided that would eliminate m = 0 or n = 0.
No. This is not random sampling as the students chose are not chosen at random. Random sampling would be something done where each sample has equal probability of being chosen. Clearly this is not random sampling.
