Let X1, X2_...., Xa be a random sample from the truncated exponential distribution with pdf f(x;0) = exp[-(x-6)],x20. Please derive the 100 1 - a % confidence interval for by a) (8 pts.) inverting the two-sided likelihood ratio test, b) (7 pts.) using the pivotal quantity method. c) (7 pts.) using the general method. d) (2 pts.) compare these intervals. If they are different which one do you prefer? Why? Let X1, X2_...., Xa be a random sample from the truncated exponential distribution with pdf f(x;0) = exp[-(x-6)],x20. Please derive the 100 1 - a % confidence interval for by a) (8 pts.) inverting the two-sided likelihood ratio test, b) (7 pts.) using the pivotal quantity method. c) (7 pts.) using the general method. d) (2 pts.) compare these intervals. If they are different which one do you prefer? Why