Let two d.f.’s, F₁(x) and F₂(x), be such that F₁(x) ≤ F₂(x) for all x . This relation referred to as the first stochastic dominance (FSD) was already considered and interpreted. Show that we can construct a sample space and probability measure on it, and two r.v.’s, X₁ and X₂ defined on this space, having the d.f. F₁(x) and F₂(x), respectively, and such that P(X₁ ≥ X₂) = 1. Is it true for any r.v.’s having the above d.f.’s?