ECE-340 Probabilistic Methods in Engineering Question 3

(3) (8 POINTS) Two bulbs are turned on at time = 0: bulb A with an average lifetime of 1,000 hrs. and bulb B with an average lifetime of 2,000 hrs. (i) What is the probability that bulb A will last longer than bulb B? (ii) What is the probability that both bulbs are still working at time t = 1,000 hrs.? (iii) Suppose that both bulbs are still working at time t = 1,000 hrs. At that time bulb B is turned off and we let bulb A work until it dies off. At that moment we turn bulb B on again and let it work until it dies off. On average, what is the length of time elapsed since bulb B was turned on for the first time until it died off? (iv) Repeat part (iii) if we exchange the roles of A and B