if (X,Y) have bivariate normal distribution N_2(0,S), S = (s_ij)

s_11 = s_22 = 1 and s_12 = s_21 = p (correlation coefficient)

is it correct to say that X,Y are both normal with N(0,1)?

furthermore, is it right to say that since p = cov(X,Y) / (s_1 * s _2) <=>

p = cov(X,Y) = E(XY) + 0 + 0 + 0 = E(x^2) = 1

???