Question: 11. Let X be uniformly distributed on (8,8 + 1),0 < 8 < 00, let [X] denote the largest integer X, and let V =

11. Let X be uniformly distributed on (8,8 + 1),0 < 8 < 00, let [X] denote the largest integer X, and let V = X - [X]. (i) The statistic V( X) is uniformly distributed on (0,1) and is therefore ancillary. (ii) The marginal distribution of [X] is given by { [8] [Xl = [8] + 1 with probability 1 - V(8) , with probability V(8) . (iii) Conditionally, given that V = v, [X] assigns probability 1 to the value [8] if V(8) v and to the value [8] + 1 if V(8) > v. [Basu (1964).]

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