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

Geometrical Domain of Spin 1/2 Probability Mass Function