Let X1,X2,,Xn be iid random variables with probability density function (pdf) as

f(x) = exp{ - (x - ) }, <<x<

• Show that X(1) = min{X1,,Xn} is sufficient.
• Show that X(1) is complete.
• Use Basu's theorem, show that X(1) and i=1n(XiX)2 are independent.