Let (Ω, F, P) be a probability space, and let X be a random variable defined on (Ω, F, P). If A is a sub σ-field of F, then E(X ∣ A) is the a.s. unique A measurable function such that, for all A ε A, ...
The constancy of the conditional expectation of some appropriate functions of order statistics on some others, is used to characterize the geometric distribution among the discrete distributions.
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