Statistics Graduate Level Quiz
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LINEAR MODELS AND GLMS
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Independent counts satisfy Yi∼Poisson⁡(μi)Y_i\sim\operatorname{Poisson}(\mu_i) with log⁡(μi)=log⁡(ti)+α+xiTβ\log(\mu_i)=\log(t_i)+\alpha+x_i^{\mathsf T}\beta, where tit_i is a known exposure. Let N=∑iYiN=\sum_iY_i.
Conditional on the observed total NN, which description of the joint distribution of the counts is correct?
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