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  • Question: N Let X1, ..., Xn denote a sample of size N, where the X; are indepen- dently (but not identically) distributed according to the binomial distribution with unknown probability parameter 2. Specifically, X; B(n;,6), 6 = 1, ..., N). (i) Show that the likelihood function for 8 belongs to the regular expo- nential family, giving the canonical parameter c() and

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N Let X1, ..., Xn denote a sample of size N, where the X; are indepen- dently (but not identically) distributed according to the binomial distribution with unknown probability parameter 2. Specifically, X; B(n;,6), 6 = 1, ..., N). (i) Show that the likelihood function for 8 belongs to the regular expo- nential family, giving the canonical parameter c() and its correspond- ing sufficient statistic T(X), where X = (X1, ..., XN)" and where x = (11, ..., In)" denotes the vector containing the observed values 1; of the X; (j = 1, ..., N).