  We investigate the flux and event rate of supernova relic neutrinos (SRNs)
and discuss their implications for the cosmic star formation rate. As reference
models, we adopt the supernova rate model based on recent observations and the
supernova neutrino spectrum numerically calculated by several groups. In the
detection energy range E_e>10 MeV, which will possibly be a background-free
region in the near future, the SRN event rate is found to be 1-2 yr^{-1} at a
water Cerenkov detector with a fiducial volume of 22.5 kton, depending on the
adopted neutrino spectrum. We also simulate the expected signal with one set of
the reference models by using the Monte Carlo method and then analyze these
pseudodata with several free parameters, obtaining the distribution of the
best-fit values for them. In particular, we use a parameterization such that
R_{SN}(z)=R_{SN}^0 (1+z)^\alpha, where R_{SN}(z) is the comoving supernova rate
density at redshift z and R_{SN}^0 and \alpha are free parameters, assuming
that the supernova neutrino spectrum and luminosity are well understood by way
of a future Galactic supernova neutrino burst or the future development of
numerical supernova simulations. The obtained 1\sigma errors for these two
parameters are found to be \delta\alpha /\alpha = 30% (7.8%) and \delta
R_{SN}^0/ R_{SN}^0 = 28% (7.7%) for a detector with an effective volume of 22.5
kton 5 yr (440 kton 5 yr), where one of the parameters is fixed. On the other
hand, if we fix neither of the values for these two parameters, the expected
errors become rather large, \delta\alpha /\alpha = 37% and \delta R_{SN}^0/
R_{SN}^0 = 55%, even with an effective volume of 440 kton 5 yr.
