  The quantum analogue of the classical characteristic function for a spin 1/2
assembly is considered and the probability mass function of the random vector
associated with the assembly is derived. It is seen that the positive regions
of Wigner and Margenau-Hill quasi distributions for the three components of
spin, correspond to a trivariate probability mass function. We identify the
domain of these positive regions as an Octahedron inscribed in the Bloch sphere
with its vertices on the surface of the sphere. It is in this domain that a
quantum characteristic function characterizing the quasi distribution, admits a
probability mass function in IR^3 . It is also observed that the classical
variates X1, X2, X3 corresponding to the 3 spin operators
\sigma_1,\sigma_2,\sigma_3 in the domain, are independent iff the Bloch vector
lies on any one of the axes.
