Question: A random variable X is said to dominate another random variable Y statewise, if X() Y() holds, for all , with strict

A random variable X is said to dominate another random variable Y statewise, if X(ω) ≥ Y(ω) holds, for all ω ∈ Ω, with strict inequality for at least one ω. Statewise dominance implies first order stochastic dominance, but the converse is not true. Construct two random variables X and Y on the probability space of a fair coin flip experiment, such that X dominates Y stochastically to first order, but no statewise dominance relation can be established.

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