Let '1'], . .. =Tn he iid PoissonUk]. Recall that the MLE for A is 1 2 Ta. (a) Findnthe Fisher information and conrm that the asymptotic variance for E is exactly Var] (which is not generally true). (h) Now suppose, for whatever reason: you want to estimate r9 = I}? What is the MLE for 6'? Use the delta method to get an asymptotic distribution for this estimator. [Note: the estimator technically does not have a nite mean, let alone nite variance! Nevertheless: the asymptotic distribution is correct] (c) Use the data provided in the data le poissonjamplersv (in the R. Files module in Canvas) to estimate A and HI. and then estimate the asymptotic standard error based on the asymptotic variance found in part (b). (d) Use the data to bootstrap an estimate of the asymptotic standard error for a. lCompare your bootstrap estimate with that of part (c)