Suppose Y1,,Yn are independent Poisson random variables with E(Yi)=i where i=exp{+Zi} depends on the levels Zi of a covariate; ,R. For instance, Zi could be the level of a drug given to the ith patient with an infectious disease and Yi could denote the number of infectious agents in a given unit of blood from the ith patient 24 hours after the drug was administered.

a) Write the model forY1,,Yn in two-parameter canonical exponential form and give the sufficient statistic.

b) Suppose =(,)T. Compute I() for the model in (a) and then find the lower bound on the variances of unbiased estimators ^ and ^ of and .