Show that the Wasserstein metric implies weak convergence; that is, if dW (Xn, X) → 0, then Xn d

→ X. Give a counterexample to show the converse is false. Prove or disprove the following claim: For random variables Xn and X with finite first moments, show that dW (Xn, X) → 0 if and only if Xn d

→ X and E(Xn) → E(X).