  We consider a simple model for active random walk with general temporal
correlations, and investigate the shape of the probability distribution
function of the displacement during a short time interval. We find that under
certain conditions the distribution is non-monotonic and we show analytically
and numerically that the existence of the non-monotonicity is governed by the
walker's tendency to move forward, while the correlations between the timing of
its active motion control the magnitude and shape of the non-monotonicity. In
particular, we find that in a homogeneous system such non-monotonicity can
occur only if the persistence is strong enough.
