An estimate is needed of the expected number of resets it takes to get a certain brand of $15amp$ ground fault protecting circuit breaker to fail to reset. A random sample of $n$ circuit breakers are each tripped and reset as many times as needed to produce a fail. The recorded numbers of resets associated with the $n$ breakers are viewed as the outcome of iid random variables $(X_1,\dots ,X_n)$.

a. Define the joint probability density of the random sample of the $n$ reset outcomes.

b. Define the MVLUE for the expected number of resets. Justify that your estimator really is a MVLUE of this proportion.

c. Is the estimator that you defined above a consistent estimator of the expected number of resets? Is it asymptotically normally distributed? 

d. Use the CRLB attainment theorem to find a MVUE of the expected number of resets, if you can. If the MVUE exists, how does it differ from the linear estimator you defined in b)?

e. Does an unbiased estimator of the variance of reset outcomes exist that achieves the CRLB, and is thereby MVUE?