  We study the properties of a homogeneous dilute Bose-Bose gas in a
weak-disorder potential at zero temperature. By using the perturbation theory,
we calculate the disorder corrections to the condensate density, the equation
of state, the compressibility, and the superfluid density as a function of
density, strength of disorder, and miscibility parameter. It is found that the
disorder potential may lead to modifying the miscibility-immiscibility
condition and a full miscible phase turns out to be impossible in the presence
of the disorder. We show that the intriguing interplay of the disorder and
intra- and interspecies interactions may strongly influence the localization of
each component, the quantum fluctuations, and the compressibility, as well as
the superfluidity of the system.
