It seems to me that the only problem with the original "selected from the set" is that it might imply a non-random selection process to some people. "Picked from the set" would be an improvement. Strictly speaking, neither "selected" nor "picked" tells you if the process was random or not, but the latter probably makes the reader more inclined to think of randomness than the former, which I think is what's being asked for.
"Drawn" definitely doesn't work because that says the selection process is random, which isn't what the OP wanted. Anything with "random" in it has the same problem.
I quite like "arbitrary" but I think it suffers a bit from the same problem. To my ear it works better if you use it to describe the selection process rather than the parameter - "a parameter arbitrarily selected from the set" rather than "an arbitrary parameter".