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4. Let y ij be observation j of a count variable for group i , i = 1 , , I , j = 1 , , n i . Suppose that Y
ij are independent Poisson with E ( Y ij ) = i . (a) Show that the ML estimate of i is ^ i = y i = j =
1 n i y ij / n i . (b) Simplify the expression for the deviance for this model.

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