Joe is a student who is conducting experiments with a series of lightbulbs. He started with 10 identical lightbulbs, each of which has an exponentially distributed lifetime with a mean of 200 hours. Joe wants to know how long it will take until the last bulb burns out (or fails). At noontime Joe stepped out to get some lunch with 6 bulbs still on. Assume that Joe came back and found that none of the 6 bulbs has failed.
a. After Joe came back, what is the expected time until the next bulb failure?
b. What is the expected length of time between the fourth bulb failure and the fifth bulb failure?