On the necessity of the statistical interpretation of the wave function

It is shown that the square the module |<|psi>|2 of the wave function psi satisfies the axiomatic definition of the probability because of the following quantal postulates: 1) States are described by normalized vectors psi of a linear space K; 2) The expansion psi=c1phi1+c2phi2 means that the system described by psi can be found either in the state phi1 or in the state hi2 (reduction postulate); 3) State vector PHI of the ensemble of the noninteracting systems S1, S2... is the direct product of the system state vectors psi1, psi2...1. So |<|psi>|2 is necessarily the probability if 1), 2), 3) are assumed and the postulate of the statis.special tical interpretation is superfluous. One can state that 1), 2), 3) give a realization of the probability theory axioms