=+24. The random variable Y stochastically dominates the random variable X provided Pr(Y ≤ u) ≤ Pr(X ≤ u) for all real u. Using quantile coupling, we can construct on a common probability space probabilistic copies Xc of X and Yc of Y such that Xc ≤ Yc with probability 1. If X has distribution function F(x) and Y has distribution function G(y), then define F[−1](u) and G[−1](u) as instructed in Example 1.5.1 of Chapter 1. If U is uniformly distributed on [0, 1], demonstrate that Xc = F[−1](U) and Yc = G[−1](U) yield quantile couplings with the property Xc ≤ Yc. Problems 19 through 23 provide examples of stochastic domination.