In the electrostatic particle simulation, the electric field is determined by the particle distribution and thus no initial condition for the electric field is needed. The equilibrium distribution function can be chosen to various forms to investigate different physical problems. In this note, a Maxwellian distribution and a two-stream Maxwellian distribution will be chosen to demonstrate the Landau damping and the two-stream instability, respectively. In the total-f simulation, the noise associated with the initial sampling of the phase space can provide initial perturbations for some physical instabilities (e.g. two-stream instability) to develop from the equilibrium state. In this case, we do not need to impose perturbation manually. However, for other cases where instability is weak or the perturbations are damping (e.g. Landau damping), manual perturbation to the particle weight is needed. In the δf simulation, we do need to manually impose perturbation on the equilibrium state. i.e. set δf to nonzero value. Otherwise δf will be always zero.