Suppose that 20 items having an exponential life distribution with an unknown rate are put on life test at various times. When the test

Suppose that 20 items having an exponential life distribution with an unknown rate λ are put on life test at various times. When the test is ended, there have been 10 observed failures — their lifetimes being (in hours) 5, 7, 6.2, 8.1, 7.9, 15, 18 , 3.9, 4.6, 5.8. The 10 items that did not fail had, at the time the test was terminated, been on test for times (in hours) 3, 3.2, 4.1, 1.8, 1.6, 2.7, 1.2, 5.4, 10.3, 1.5. If prior to the testing it was felt that λ could be viewed as being a gamma random variable with parameters (2, 20), what is the Bayes estimator of λ?