Let's say I have a random variable A, that is uniform on [0,b], where b is a positive integer. Then, I have another r.v. D that is A minus the floor function of A. In other words D is the fractional part of A. For instance for values a = 0.2, a = 1.2 it means that D will take the same value 0.2, and in similar way for any other fractional part. If I understand correctly, this means that D is uniform between 0 and 1, while it can never take the value 1. Now if I where to look at the PDF of d, could I argue that f_d(d) > 0 for every d in (0,x), where x equals 1