Question: 32. Negative binomial. Let X, Y be independently distributed according to negative binomial distributions Nbt p-; m) and Nb(P2' n) respectively, and let qi =

32. Negative binomial. Let X, Y be independently distributed according to negative binomial distributions Nbt p-; m) and Nb(P2' n) respectively, and let qi = 1 - Pi' (i) There exists a UMP unbiased test for testing H : °= q2/ql :::;; 00 and hence in particular H' :PI s P2 . (ii) Determine the conditional distribution required for testing H' when m=n=l.

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