The lifetime X of an electric lamp has the simple exponential survival function A factory has n lamps which are lighted day and night, and every week the burnt out ones are replaced by new ones. At...

The lifetime X of an electric lamp has the simple exponential survival function

A factory has n lamps which are lighted day and night, and every week the burnt out ones are replaced by new ones. At a particular inspection time, it was observed that out of n, n₁
were dead, and n − n₁
= n₂
were still alive. Find out a BAN estimator of θ based on this data set. Obtain the Fisher information on θ from this binary model as well as from the ideal situation when X₁,...,X_n
would have been all observed. Compare the two and comment on the loss of information due to this grouping.