The probability density function used in making the phase-space sampling can be any reasonable function, which can be chosen to obtain desired resolution of the phase-space. The most intuitive way of sampling the phase-space is to sample it using the uniform probability density function, i.e., p(Z) = 1∕V , where V is the total volume of the phase space. Another frequently used sampling scheme is to load particle markers according to the initial total distribution function of the physical particles. In this case P(Z) = ftot(Z)∕Ns, where Ns is the total number of physical particles, i.e., ∫ V ftot(Z)dΓ = Ns. (The method of generating random markers that satisfies a given probability density function is discussed in Sec. 7.)