Owing to its high quantum efficiency, the charge-coupled device (CCD) is an important imaging tool employed in biological applications such as single molecule microscopy. Under extremely low light conditions, however, a CCD is generally unsuitable because its readout noise can easily overwhelm the weak signal. Instead, an electron-multiplying charge-coupled device (EMCCD), which stochastically amplifies the acquired signal to drown out the readout noise, can be used. We have previously proposed a framework for calculating the Fisher information, and hence the Cramer-Rao lower bound, for estimating parameters (e.g., single molecule location) from the images produced by an optical microscope. Here, we develop the theory that is needed for deriving, within this framework, performance measures pertaining to the estimation of parameters from an EMCCD image. Our results allow the comparison of a CCD and an EMCCD in terms of the best accuracy with which parameters can be estimated from their acquired images.