In what situations does the difference between random numbers generated on [0,1) and those generated on [0,1] make a difference?



I'm used to pseudo random number generators that return floating point values in the half open interval [0,1).


I've seen some reference to RNGs that can return values on the closed interval [0,1], e.g. this implementation of the Mersenne Twister.


I can see reasons why you'd want to exclude one, or both, of the endpoints for mathematical reasons, e.g.


exponentially_distributed=-logf( 1.0-rng() )


always yields a valid number if 0.0<=rng()<1.0.


But I can't think of a case where replacing an rng yielding [0,1] with one that yields [0,1) would produce any practi


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