  A DNA polymerase (DNAP) replicates a template DNA strand. It also exploits
the template as the track for its own motor-like mechanical movement. In the
polymerase mode it elongates the nascent DNA by one nucleotide in each step.
But, whenever it commits an error by misincorporating an incorrect nucleotide,
it can switch to an exonuclease mode. In the latter mode it excises the wrong
nucleotide before switching back to its polymerase mode. We develop a
stochastic kinetic model of DNA replication that mimics an {\it in-vitro}
experiment where a single-stranded DNA, subjected to a mechanical tension $F$,
is converted to a double-stranded DNA by a single DNAP. The $F$-dependence of
the average rate of replication, which depends on the rates of both polymerase
and exonuclease activities of the DNAP, is in good qualitative agreement with
the corresponding experimental results. We introduce 9 novel distinct {\it
conditional dwell times} of a DNAP. Using the methods of first-passage times,
we also derive the exact analytical expressions for the probability
distributions of these conditional dwell times. The predicted $F$-dependence of
these distributions are, in principle, accessible to single-molecule
experiments.
