  Before a cell divides into two daughter cells, chromosomes are replicated
resulting in two sister chromosomes embracing each other. Each sister
chromosome is bound to a separate proteinous structure, called kinetochore
(kt), that captures the tip of a filamentous protein, called microtubule (MT).
Two oppositely oriented MTs pull the two kts attached to two sister chromosomes
thereby pulling the two sisters away from each other. Here we theoretically
study an even simpler system, namely an isolated kt coupled to a single MT;
this system mimics an {\it in-vitro} experiment where a single kt-MT attachment
is reconstituted using purified extracts from budding yeast. Our models not
only account for the experimentally observed "catch-bond-like" behavior of the
kt-MT coupling, but also make new predictions on the probability distribution
of the lifetimes of the attachments. In principle, our new predictions can be
tested by analyzing the data collected in the {\it in-vitro} experiments
provided the experiment is repeated sufficiently large number of times. Our
theory provides a deep insight into the effects of (a) size, (b) energetics,
and (c) stochastic kinetics of the kt-MT coupling on the distribution of the
lifetimes of these attachments.
