Suppose that the joint p.d.f. of two random variables X and Y is proportional, as a function of (x, y), to
exp−[ax2 + by2 + cxy + ex + gy + h],
where a > 0, b > 0, and c, e, g, and h are all constants. Assume that ab > (c/2)2. Prove that X and Y have a bivariate normal distribution, and find the means, variances, and correlation.