  We study the problem of particle indistinguishability for the three cases
known in nature: identical classical particles, identical bosons and identical
fermions. By exploiting the fact that different types of particles are
associated with Hilbert space vectors with different symmetries, we establish
some relations between the expectation value of several different operators, as
the particle number one and the interparticle correlation one, evaluated for
states of a pair of identical (a) classical particles, (b) bosons and (c)
fermions. We find that the quantum behavior of a pair of identical classical
particles has exactly half fermionic and half bosonic characteristics.
