  This paper offers examples of concrete numerical applications of Bayesian
quantum-state-assignment methods to a three-level quantum system. The
statistical operator assigned on the evidence of various measurement data and
kinds of prior knowledge is computed partly analytically, partly through
numerical integration (in eight dimensions) on a computer. The measurement data
consist in absolute frequencies of the outcomes of N identical von Neumann
projective measurements performed on N identically prepared three-level
systems. Various small values of N as well as the large-N limit are considered.
Two kinds of prior knowledge are used: one represented by a plausibility
distribution constant in respect of the convex structure of the set of
statistical operators; the other represented by a Gaussian-like distribution
centred on a pure statistical operator, and thus reflecting a situation in
which one has useful prior knowledge about the likely preparation of the
system.
  In a companion paper the case of measurement data consisting in average
values, and an additional prior studied by Slater, are considered.
