8.26 Let (Xn, Yn) have a bivariate normal distribution with means E(Xn) = E(Yn) = 0, variances E(X2 n) = E(Y 2 n ) = 1, and with correlation coefficient ρn tending to 1 as n → ∞.

(a) Show that (Xn, Yn) L

→ (X, Y ) where X is N(0, 1) and P(X = Y ) = 1.

(b) If S = {(x, y) : x = y}, show that (8.25) does not hold.