  This paper characterizes the optimal type-II error exponent for a distributed
hypothesis testing-against-independence problem when the \emph{expected} rate
of the sensor-detector link is constrained. Unlike for the well-known
Ahlswede-Csiszar result that holds under a \emph{maximum} rate constraint and
where a strong converse holds, here the optimal exponent depends on the allowed
type-I error exponent. Specifically, if the type-I error probability is limited
by $\epsilon$, then the optimal type-II error exponent under an \emph{expected}
rate constraint $R$ coincides with the optimal type-II error exponent under a
\emph{maximum} rate constraint of $(1-\epsilon)R$.
