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An uncertain variable is an aleatory variable in a decision basis or in an informational problem statement (eg, length of life or future stock price). The term uncertain variable is commonly used in decision analysis to denote both continuous variables and discrete events. In the degenerate case, where its associated probability distribution is concentrated on a single point, the uncertain variable can be treated as a deterministic variable; this degenerate case is excluded by referring to the uncertain variable as a stochastic variable. In decision bases, some uncertain variables arise as a consequence of the domain in which the decision is being made, while others result from the decision-maker’s unique information and circumstances.

See also: decision domain and decision situation.