5 (i) Let x,, ..., x„ be a random sample from x„) is sufficient for 0? the PDF f(x: 0). What is meant by saying that 1(x,, .. Let e-(x-0). x> 0, S(x: 0) = and suppose n= 3. Let y, < y, < y; be ordered values of x. x. X. Show that sufficient for 0. is (ii) Show that the distribution of Y, - 0 is exponential of parameter 3. Your client suggests the following possibilities as estimators of 0: 0, = x, – 1. 02 = y1, 0, = }(x, +x, + x3) – 1. How would you advise him? Hint: General theorems used should be clearly stated, but need not be proved.

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