6 The lifetime of a battery is believed to be exponentially

6. The lifetime of a battery is believed to be exponentially distributed with parameter lambda. 30 batteries are tested and last for the following times: 1.2, 1.3. 1.5, 1.8, 1.9, 2.2, 2.4, 2.5, 2.7, 3.0, 3.5, 3.7, 4.1, 4.4, 4.8, 5.3, 5.7, 6.0, 6.8, 7.2, 7.8, 8.3, 8.9, 9.4, 9.7, 10.3, 11.2, 11.9, 12.5. and 12.9 (a) What is the maximum likelihood estimate for lambda? (b) Show that [0.1128, 0.2478] is a 10% likelihood interval for lambda. (c) If the data are censored at 3.5, what is the new maximum likelihood estimate for lambda? (d) Which of the following is a 10% likelihood interval for lambda for the censored data: (i) [0.1128, 0.2478] (ii) [0.0585, 0.1788] (iii) [0.0514, 0.2033] (iv) [0.0514, 0.1788] (v) [0.585, 0.2033]

Solution

i will answer d) (v) [0.585, 0.2033]