Question: Let X1, ...,XN be a random sample from a multinomial distribution with three possible outcomes: O1,O2,O3 and their corresponding probabilities: p1,p2, 1 p1

Let X1, ...,XN be a random sample from a multinomial distribution with three possible outcomes: O1,O2,O3 and their corresponding probabilities: p1,p2, 1 − p1 − p2.

Obtain a UMPU test of a H0 : p1 ≤ p2 against the alternative H1 : p1 > p2 knowing that among N observation, outcomes O1,O2, and O3 were observed n1,n2, and N − n1 − n2 times, respectively

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