> On Jul 16, 2020, at 1:28 PM, Roger Hui <[email protected]> wrote:
> 
> Is it valid to generate ?m$p where p>q, and keep only the numbers which are
> less than q?  (Not less than p.)
> 

Yes.
You can view this as a special case of rejection sampling,
https://en.wikipedia.org/wiki/Rejection_sampling
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