In the neoclassical model of consumer behavior, considerable work has been done investigating when a consumer's demand behavior can be described as having been derived from utility maximization. However, most discussions are in a certainty world. We expand on prior analyses in an uncertainty setting by providing conditions under which contingent claim and asset demands will be consistent with state independent Expected Utility maximization. The question is addressed using two different traditional approaches. First given the analytical form of the demand functions, we derive necessary and sufficient conditions such that the consumer's behavior can be rationalized by an Expected Utility function. Second, we provide a necessary and sufficient condition for a finite set of observations on prices, probabilities and quantities to be consistent with Expected Utility maximization for the case of a single commodity in each state. This condition is shown to be analogous to the strong axiom of revealed preference in classical certainty demand theory. For both approaches, we consider the complete and incomplete asset market cases.