Consider a random sample X₁, X₂, ..., X_n from an exponential distribution with threshold parameter

Problem B.3. Consider a random sample X1, X2, ..., Xn from an exponential distribu- tion with threshold parameter 7 > 0 unknown, that is, f (20; n) = e - (20 - n), x27; 0 otherwise. (a) Show that Q = min {X1, X2, ..., Xn} -n is a pivotal quantity and find its distri- bution. (b) Using Q from (a), derive a 1 - a two-sided equal-tail confidence interval for n