  (abridged) The signal-to-noise ratio (SNR) is used in gravitational-wave
observations as the basic figure of merit for detection confidence and,
together with the Fisher matrix, for the amount of physical information that
can be extracted from a detected signal. SNRs are usually computed from a
sensitivity curve, which describes the gravitational-wave amplitude needed by a
monochromatic source of given frequency to achieve a threshold SNR. For
interferometric space-based detectors similar to LISA, which are sensitive to
long-lived signals and have constantly changing position and orientation, exact
SNRs need to be computed on a source-by-source basis. For convenience, most
authors prefer to work with sky-averaged sensitivities, accepting inaccurate
SNRs for individual sources and giving up control over the statistical
distribution of SNRs for source populations. In this paper, we describe a
straightforward end-to-end recipe to compute the non-sky-averaged sensitivity
of interferometric space-based detectors of any geometry: in effect, we derive
error bars for the sky-averaged sensitivity curve, which provide a stringent
statistical interpretation for previously unqualified statements about
sky-averaged SNRs. As a worked-out example, we consider isotropic and
Galactic-disk populations of monochromatic sources, as observed with the
"classic LISA" configuration. We confirm that the (standard) inverse-rms
average sensitivity for the isotropic population remains the same whether or
not the LISA orbits are included in the computation. However, detector motion
tightens the distribution of sensitivities, so for 50% of sources the
sensitivity is within 30% of its average. For the Galactic-disk population, the
average and the distribution of the sensitivity for a moving detector turn out
to be similar to the isotropic case.
