  Quantum transport of electrons through a molecule is a series of individual
electron tunnelling events separated by stochastic waiting time intervals. We
study the emergence of temporal correlations between successive waiting times
for the electron transport in a vibrating molecular junction. Using master
equation approach, we compute joint probability distribution for waiting times
of two successive tunnelling events. We show that the probability distribution
is completely reset after each tunnelling event if molecular vibrations are
thermally equilibrated. If we treat vibrational dynamics exactly without
imposing the equilibration constraint, the statistics of electron tunnelling
events become non-renewal. Non-renewal statistics between two waiting times
$\tau_1$ and $\tau_2$ means that the density matrix of the molecule is not
fully renewed after time $\tau_1$ and the probability of observing waiting time
$\tau_2$ for the second electron transfer depends on the previous electron
waiting time $\tau_1$. The strong electron-vibration coupling is required for
the emergence of the non-renewal statistics. We show that in Franck-Condon
blockade regime the extremely rare tunnelling events become positively
correlated.
