  We have formulated the scattering theory on Majorana fermions emerging in the
surface bound state of the superfluid $^3$He B-phase ($^3$He-B) by an impurity.
By applying the theory to the electron bubble, which is regarded as the
impurity, trapped below a free surface of $^3$He-B, the observed mobility of
the electron bubble [Ikegami et al., J. Phys. Soc. Jpn. 82, 124607 (2013)] is
quantitatively reproduced. The mobility is suppressed in low temperatures from
the expected value in the bulk $^3$He-B by the contribution from the surface
Majorana fermions. By contrast, the mobility does not depend on trapped depth
of the electron bubble in spite of the spatial variation of the wave function
of the surface Majorana fermions. Our formulated theory demonstrates the depth
independent mobility by considering intermediate states in the scattering
process. Therefore, we conclude that the experiment has succeeded in observing
Majorana fermions in the surface bound state.
