Daniel and Seema are exploring a cave, and each have brought a flashlight. The lifetimes of their flashlight batteries can be considered independent exponential random variables with rate parameters s λd (where D denotes Daniel and S denotes Seema). Suppose one of their batteries has just gone out. What is the expected additional lifetime of the other person's battery?
A) Solve for the remaining lifetime in terms of λD and λS. Show all work and come up with a general formula.
B) Suppose Daniel's flashlight battery lasts, on average, for 43 hours and Seema's for 52 hours, on average. Given that one of their flashlights has just gone out, how long do we expect the other flashlight battery to last?