We study the distribution of noise in images synthesized by radio interferometers, focusing particularly on the noise due to source power fluctuations. For a total power interferometer, the r.m.s. fluctuation in the image consists of a term that is constant all over the map, which is the uncorrelated system noise divided by the number of telescopes in the interferometer, and a term that is the image itself. For a correlation interferometer the expression is not so simple but is qualitatively similar. Our results are consistent with intuitive expectations in various observing situations. We find similarities in self-noise at optical and radio wavelengths.