Probability distribution for the quantum universe

We determine the inner product on Hilbert space of wavefunctions universe by imposing Hermiticity quantum Hamiltonian in context minisuperspace model. The corresponding probability density reproduces successfully classical distribution $\hbar \to 0$ limit, for closed universes filled with a perfect fluid index $w$. When $-1/3<w\le 1$, wavefunction is normalizable and becomes vanishingly small at big bang/big crunch singularities, least semi-classical level. Quantum expectation values physical geometrical quantities, which diverge classically are shown to be finite.