Bulbs Still Burning at the Deadline
Six bulbs have independent lifetimes that are exponentially distributed with unknown rate λ (per hour). They are all switched on together and the test is stopped at 12 hours. Three bulbs failed, at 2, 5 and 9 hours. The other three were still working when the test stopped. What is the maximum likelihood estimate of the mean lifetime 1/λ, in hours? Give an exact fraction.
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Source: Standard censored-lifetime exercise from reliability statistics. Statement written for AxiomIQ.