Consider a random sample of size n from an exponential distribution, Xi ~ EXP(1,eta).
a) Show that Q = X1:n - eta is a pivotal quantity and find its distribution.
b) Derive a 100(gamma)% equal tailed confidence interval for eta.
c) The following data are mileages for 19 military personnel carriers that failed in service: 162, 200, 271, 320, 393, 508, 539, 629, 706, 777, 884, 1008, 1101, 1182, 1463, 1603, 1984, 2355, 2880. Assuming that these data are observations of a random sample from an exponential distribution, find a 90% confidence interval for eta. Assume that theta = 850 is known.