  We propose an approach for probing Majorana bound states (MBSs) in a nanowire
via counting statistics of a nearby charge detector in the form of a
single-electron transistor (SET). We consider the impacts on the counting
statistics by both the local coupling between the detector and an adjacent MBS
at one end of a nanowire and the nonlocal coupling to the MBS at the other end.
We show that the Fano factor and the skewness of the SET current are minimized
for a symmetric SET configuration in the absence of the MBSs or when coupled to
a fermionic state. However, the minimum points of operation are shifted
appreciably in the presence of the MBSs to asymmetric SET configurations with a
higher tunnel rate at the drain than at the source. This feature persists even
when varying the nonlocal coupling and the pairing energy between the two MBSs.
We expect that these MBS-induced shifts can be measured experimentally with
available technologies and can serve as important signatures of the MBSs.
