In the notation of Exercise 6.18, show that the second derivative of K*(x, 1 − x; 1/2) at x = 1/2 is 8, whereas the conditional variance of X1 given that X1

+ X2 = 1 is 1/12. Hence deduce that the double saddlepoint approximation to the conditional density of X1 is not the same as applying the ordinary saddlepoint approximation directly to the conditional cumulant generating function of X1.