The change-of-variables theorem of probability theory is applied to compute acoustic field and array beam power probability density functions (pdfs) in uncertain ocean environments represented by stratified, attenuating ocean waveguide models. Computational studies for one and two-layer waveguides investigate the functional properties of the acoustic field and array beam power pdfs. For the studies, the acoustic parameter uncertainties are represented by parametric pdfs. The field and beam response pdfs are computed directly from the parameter pdfs using the normal-mode representation and the change-of-variables theorem. For two-dimensional acoustic parameter uncertainties of sound speed and attenuation, the field and beam power pdfs exhibit irregular functional behavior and singularities associated with stationary points of the mapping, defined by acoustic propagation, from the parameter space to the field or beam power space. Implications for the assessment of orthogonal polynomial expansion and other methods for computing acoustic field pdfs are discussed.