  We constrain the average episodic quasar lifetime (as in steady-state
accretion) using two statistics of quasars that are recently turned off (i.e.,
dimmed by a large factor): 1) the fraction of turned-off quasars in a
statistical sample photometrically observed over an extended period (e.g.,
$\Delta t=20$ yrs); 2) the fraction of massive galaxies that show 'orphan'
broad MgII emission, argued to be short-lived echoes of recently turned-off
quasars. The two statistics constrain the average episodic quasar lifetime to
be hundreds to thousands of years. Much longer (or shorter) episodic lifetimes
are strongly disfavored by these observations. This average episodic lifetime
is broadly consistent with the infall timescale (viscous time) in the standard
accretion disk model for quasars, suggesting that quasar episodes are governed
by accretion disk physics rather than by the gas supply on much larger scales.
Compared with the cumulative quasar lifetime of $\sim 10^6-10^8\,$yrs
constrained from quasar clustering and massive black hole demographics, our
results suggest that there are $\sim 10^3-10^5$ episodes of quasar accretion
during the assembly history of the supermassive black hole. Such short episodes
should be clustered over intervals of $\sim 10^4\,$yrs to account for the sizes
of ionized narrow-line regions in quasars. Our statistical argument also
dictates that there will always be a small fraction of extreme variability
quasars caught in 'state transitions' over multi-year observing windows,
despite the much longer episodic lifetime. These transitions could occur in a
rather abrupt fashion during non-steady accretion.
