  The thermodynamic uncertainty relation (TUR) provides a universal entropic
bound for the precision of the fluctuation of the charge transfer for example
for a class of continuous time stochastic processes. However, its extension to
general nonequilibrium dynamics is still an unsolved problem. In this Letter,
we show TUR for an arbitrary finite time in terms of exchange fluctuation
theorem applied to ensemble of copies of the original system by assuming a
physical regularity condition for the probability distribution. As a nontrivial
practical consequence, we obtain universal scaling relations among the mean and
variance of the charge transfer in short time regime. In this manner, we can
deepen our understanding on a link between two important rigorous relations,
i.e., the fluctuation theorem and the thermodynamic uncertainty relation.
