  A beam splitter consisting of two normal leads coupled to one end of a
topological superconducting nanowire via double quantum dot is investigated. In
this geometry, the linear current cross-correlations at zero temperature change
signs versus the overlap between the two Majorana bound states hosted by the
nanowire. Under symmetric bias voltages the net current flowing through the
nanowire is noiseless. These two features highlight the fermionic nature of
such exotic Majorana excitations though they are based on the
superconductivity. Moreover, there exists a unique local particle-hole symmetry
inherited from the self-Hermitian property of Majorana bound states, which is
apparently scarce in other systems. We show that such particular symmetry can
be revealed through measuring the currents under complementary bias voltages.
