The effects of a randomly oriented anisotropy on relaxation phenomena including the memory effect of a noninteracting magnetic nanoparticle assembly, are numerically studied with a localized partition function and a master equation, leading to the following results. During the zero-field-cooled (ZFC) process, the energy barrier histogram changes with temperature, while during the field-cooled (FC) process it remains stable. In the relaxation process after ZFC initialization, the effective energy barrier distribution, which is derived from the Tln
(t/τ0) (T temperature, t time, and τ0 characteristic time constant) scaling curve, only reflects the low-energy region of the energy barrier histogram. The memory effect with temporary cooling during time evolution occurs in the studied assembly even without volume distribution and particle interaction involved.