Following the MLE method, the information matrix is closely related with the asymptotic variance of MLE. For the MLE of Poisson distribution,

(a) First compute the Fisher information matrix then plug in the MLE \(\hat{\lambda}\) to estimate the variance of \(\widehat{\lambda}\).

(b) Plug in \(\widehat{\lambda}\) in the observed Fisher information matrix to estimate the variance of \(\widehat{\lambda}\).

(c) Compare part(a) and (b).