  We investigate, by means of extensive Monte Carlo simulations, the magnetic
critical behavior of the three-dimensional bimodal random-field Ising model at
the strong disorder regime. We present results in favor of the two-exponent
scaling scenario, $\bar{\eta}=2\eta$, where $\eta$ and $\bar{\eta}$ are the
critical exponents describing the power-law decay of the connected and
disconnected correlation functions and we illustrate, using various finite-size
measures and properly defined noise to signal ratios, the strong violation of
self-averaging of the model in the ordered phase.
