statistics
Let X 1,X2, X3, X4, X5 be the order statistics of a random sample of size 5 from a
rectangular R(0, θ) distribution.
(i) Show that 3X2 is an UE of θ .
(ii) Find the joint distribution of X2 and X5
.(iii) Show that X5 is a sufficient statistic for θ .
(iv) Find the conditional expectation E (3X2 | x5 ) =Φ(x5).
(v) Compare the variance of 3X2 and Φ(X5).
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