To improve the ability of quickly and effectively resolving the coupling of electrically large complex cavities (microwave chaotic cavities), the statistical properties of the scattering from these cavities have been studied by using a statistical electromagnetics method. Firstly, based on the antenna theory, the input impedance expression of cavities is established by using the expanded electromagnetic eigenmode expression. Secondly, the random coupling model (RCM) is introduced from wave chaos theory and statistical method about microwave chaotic cavities. It is simply to use this method to directly obtain the three-dimensional model. Lastly, the three-dimensional Sinai microwave chaotic cavity is designed, and used to carry out the numerical experiment. Their statistical properties obtained are agreed well with one-another between the numerical result and RCM one. Importantly, the RCM, which is a very good method to be able to quickly predict the sensitivity of coupling about the microwave chaotic cavities, is independent of the details of the cavities.