  In this note, by an elementary use of Girsanov's transform we show that the
exit time for either a biased random walk or a drifted Brownian motion on a
symmetric interval is stochastically monotone with respect to the drift
parameter. In the random walk case, this gives an alternative proof of a recent
result of E. Pek\"oz and R. Righter in 2024. Our arguments in both discrete and
continuous cases are parallel to each other. We also outline a simple SDE proof
for the Brownian case based on a standard comparison theorem.
