(Solution Download) If X1 Xn are iid with pdf f x e x I

If X1,... ,Xn are iid with pdf f(x|?) = e-(x-?)I[?,?) (x), then Y = min{X1,... ,Xn} is sufficient for ? with pdf
fY(y|?) = ne-n(y-?) I[?,?)(y)
In Example 9.2.13 a 1 - ? confidence interval for ? was found using the method of Section 9.2.3. Compare that interval to 1 - ? intervals obtained by likelihood and pivotal methods.