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Abstract

We derive a Fisher matrix for the parameters characterising a population of
gravitational-wave events. This provides a guide to the precision with which
population parameters can be estimated with multiple observations, which
becomes increasingly accurate as the number of events and the signal-to-noise
ratio of the sampled events increases. The formalism takes into account
individual event measurement uncertainties and selection effects, and can be
applied to arbitrary population models. We illustrate the framework with two
examples: an analytical calculation of the Fisher matrix for the mean and
variance of a Gaussian model describing a population affected by selection
effects, and an estimation of the precision with which the slope of a power law
distribution of supermassive black-hole masses can be measured using
extreme-mass-ratio inspiral observations. We compare the Fisher predictions to
results from Monte Carlo analyses, finding very good agreement.