  The path integral technique is used to derive a possible expression for the
density operator of the fermionic harmonic oscillator. In terms of the
Grassmann variables, the fermionic density operator can be written as: $\rho_F
(\beta)=c^* (\beta)c(\beta) \pm c^*(\beta)c(\beta)e^{-\beta\omega}$, where +(-)
means that the sum over all antiperiodic (periodic) orbits. Our density
operator is then used to obtain the usual fermionic partition function which
describes the fermionic oscillator in thermal equilibrium. Also, according to
the periodic orbit $c(\beta)=c(0)$, the graded fermionic partition function is
obtained.
