  Suppose that we are given an infinite binary sequence which is random for a
Bernoulli measure of parameter $p$. By the law of large numbers, the frequency
of zeros in the sequence tends to~$p$, and thus we can get better and better
approximations of $p$ as we read the sequence. We study in this paper a similar
question, but from the viewpoint of inductive inference. We suppose now that
$p$ is a computable real, but one asks for more: as we are reading more and
more bits of our random sequence, we have to eventually guess the exact
parameter $p$ (in the form of a Turing code). Can one do such a thing uniformly
on all sequences that are random for computable Bernoulli measures, or even on
a `large enough' fraction of them? In this paper, we give a negative answer to
this question. In fact, we prove a very general negative result which extends
far beyond the class of Bernoulli measures.
