A production lot of five electronic components is to be tested to determine (J, the mean lifetime. A sample of five components is drawn, and the lifetimes X 1 ... , X 5 are observed. It is known that...

A production lot of five electronic components is to be tested to determine (J, the mean lifetime. A sample of five components is drawn, and the lifetimes X₁
... , X₅
are observed. It is known that are observed. It is known that
  From past records it is known that, among production lots, (J is distributed according to an (10, 0.01) distribution. The five observations are 15, 12, 14, 10, 12. Find the generalized maximum likelihood estimate of (J, the posterior mean of (J, and their respective posterior variances.