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But whatI've seen papers saying that there are no tests for randomness, only for non-randomness. As far as I know, that is the situation.
is the general precondition of randomness of of x(i) in a our
laboratory samples? I do not remember how to answer this quesion.
I know that a distribution of <x> approaches a Gaussian shape, evenThis is a misconception. There are many distributions that become Gaussian in the large N limit, but not all. The chi-squared distribution is an example of one that does not.
when distributions of x(i), in each sample, are not Gaussian, when the
number of samples approaches infinity.
--"Trust me. I have a lot of experience at this."