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The effects of detector wobble motion on image variance is described analytically and verified by simulation studies. Simulation results in the form of variance images are presented for various phantoms, sampled under both uniform and wobble-motion conditions. It is shown that under most measurement conditions in a typical PET study, the image precision is degraded due to the nonuniform projection variance introduced by the wobble motion. Using the wobble parameters of the UBC-TRIUMF development of PETT VI, the rms noise is found to be increased by 9 percent due to wobbling.