  Brownian yet non-Gaussian diffusion has recently been observed in numerous
biological and active matter system. The cause of the non-Gaussian distribution
have been elaborately studied in the idea of a superstatistical dynamics or a
diffusing diffusivity. Based on a random diffusivity model, we here focus on
the ergodic property and the scatter of the amplitude of time-averaged
mean-squared displacement (TAMSD). Further, we individually investigate this
model with three categories of diffusivities, including diffusivity being a
random variable $D$, a time-dependent but uncorrelated diffusivity $D(t)$, and
a correlated stochastic process $D(t)$. We find that ensemble-averaged TAMSDs
are always normal while ensemble-averaged mean-squared displacement can be
anomalous. Further, the scatter of dimensionless amplitude is determined by the
time average of diffusivity $D(t)$. Our results are valid for arbitrary
diffusivities.
