  This work considers the inclusion detection problem of electrical impedance
tomography with stochastic conductivities. It is shown that a conductivity
anomaly with a random conductivity can be identified by applying the
Factorization Method or the Monotonicity Method to the mean value of the
corresponding Neumann-to-Dirichlet map provided that the anomaly has high
enough contrast in the sense of expectation. The theoretical results are
complemented by numerical examples in two spatial dimensions.
