Sourced Friedmann equations with holographic energy density

We reexamine cosmological applications of the holographic energy density in the framework of sourced Friedmann equations. These equations are useful to find the equation of state for a system with IR cutoff. In the case that the IR cutoff is taken to be the Hubble horizon, it is found that the equations of state for the holographic energy density is not $\omega_{\rm \Lambda}=0$ but it is indeterminate. In this case the continuity equation plays an important role. Also we discuss a possibility of the holographic energy density being static with the fixed equation of state $\omega_{\rm \Lambda}=-1$.