  In this paper, we show that the mixed fractional Poisson process (MFPP)
exhibits the long-range dependence (LRD) property. It is proved by establishing
an asymptotic result for the covariance of inverse mixed stable subordinator.
Also, it is shown that the increments of the MFPP, namely, the mixed fractional
Poissonian noise (MFPN) has the short-range dependence (SRD) property.
