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When testing a set of data for randomness according to a probabilitydistribution that depends on a parameter, access to this parameter can beconsidered as a computational resource. We call a randomness test Hippocraticif it is not permitted to access this resource. In these terms, we show thatfor Bernoulli measures $\mu_p$, $0\le p\le 1$ and the Martin-L\"of randomnessmodel, Hippocratic randomness of a set of data is the same as ordinaryrandomness. The main idea of the proof is to first show that fromHippocrates-random data one can Turing compute the parameter $p$. However, weshow that there is no single Hippocratic randomness test such that passing thetest implies computing $p$, and in particular there is no universal Hippocraticrandomness test.

The probability distribution as a computational resource for randomness testing