  Generalization of the Lambalgen's theorem is studied with the notion of
Hippocratic (blind) randomness without assuming computability of conditional
probabilities. In [Bauwence 2014], a counter-example for the generalization of
Lambalgen's theorem is shown when the conditional probability is not
computable. In this paper, it is shown that (i) finiteness of martingale for
blind randomness, (ii) classification of two blind randomness by likelihood
ratio test, (iii) sufficient conditions for the generalization of the
Lambalgen's theorem, and (iv) an example that satisfies the Lambalgen's theorem
but the conditional probabilities are not computable for all random parameters.
