It is assumed that the number of times a light$-$rail transit wagon registers a system error when it runs an

entire length of track follows a Po$($ distribution. A random sample of $n$ runs, assuming the runs are

independent, is observed.

a$.$ Suppose the target parameter is the probability that no more than $1$ system error will be observed.

Define such as a function $$ of the $($basic$)$ parameter $$

b$.$ Find an unbiased estimator for $.$

c$.$ Get the MLE for $$

d$.$ Find the asymptotic distribution of your MLE in $($c$).$