Question: Let X 1 , X 2 , , X n be iid random variables with probability density function (pdf) as f ( x ) =

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.

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