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We analyze the sensitivity of a network of interferometer gravitational-wavedetectors to the gravitational-wave stochastic background, and derive thedependence of this sensitivity on the orientations of the detector arms. Webuild on and extend the recent work of Christensen, but our conclusion for theoptimal choice of orientations of a pair of detectors differs from his. For apair of detectors (such as LIGO) that subtends an angle at the center of theearth of $\,\alt 70^\circ$, we find that the optimal configuration is for eachdetector to have its arms make an angle of $45^\circ$ (modulo $90^\circ$) withthe arc of the great circle that joins them. For detectors that are fartherseparated, each detector should instead have one arm aligned with this arc. Wealso describe in detail the optimal data-analysis algorithm for searching forthe stochastic background with a detector network, which is implicit in earlierwork of Michelson. The LIGO pair of detectors will be separated by $\sim 3000\, {\rm km}$. The minimum detectable stochastic energy-density for thesedetectors with their currently planned orientations is $\sim 3\%$ greater thanwhat it would be if the orientations were optimal.Comment: 56 pages, 10 figures, Caltech preprint GRP-347, submitted to Phys Rev  D, uses revtex macro

Sensitivity of the Laser Interferometer Gravitational Wave Observatory to a stochastic background, and its dependence on the detector orientations