Randomness is about having a uniform probability of results, but that does not translate into a uniform distribution of results, nor can it, because of the de-correlation between random results. Specifically, the chance of getting the same result multiple times is non-zero, and actually can be fairly high with a lot of samples, whereas the chance of duplicate results in a uniform distribution is zero.
Randomness is about having a uniform probability of results
Well, you're still assuming the colloquial definition of "random," which implies "uniformly random." Of course, we can have a random process that is not uniformly random.
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Randomness is about having a uniform probability of results, but that does not translate into a uniform distribution of results, nor can it, because of the de-correlation between random results. Specifically, the chance of getting the same result multiple times is non-zero, and actually can be fairly high with a lot of samples, whereas the chance of duplicate results in a uniform distribution is zero.
Read the article for more details and examples.
Randomness is about having a uniform probability of results
Well, you're still assuming the colloquial definition of "random," which implies "uniformly random." Of course, we can have a random process that is not uniformly random.