It is well known that the acoustic transfer function (Green's function) of an ocean waveguide from a particular source position to a particular receiver position may depend sensitively on environmental parameters such as sound-speed profiles and bathymetry. On the other hand, it might reasonably be hypothesized that a large ensemble of acoustic transfer functions, indexed by source position, is in some statistical sense not highly sensitive to details of the acoustic environment. Such ensembles are important in predicting statistical variations of both signal and noise responses for broadband sonar systems. Since the acoustic environment is never known exactly, the sensitivity question needs to be addressed. This question may be investigated by estimating the probability density associated with an ensemble and the variation of this probability density with environmental parameters. In this work, an observation-space partitioning process [J. Acoust. Soc. Am. 96, 3312(A) (1994)] is applied to estimate the probability densities and investigate the sensitivity of ensembles of both acoustic transfer functions and received transients to environmental parameters. Implications for training of classifiers for automated recognition of acoustic transients are discussed.