The life length Y (in hundreds of hours) for fuses used in a tele video computer terminal has an exponential distribution with mean β = 5. Each terminal requires two such fuses—one acting as a backup that comes into use only when the first fuse fails.
a. If two such fuses have independent life lengths X and Y, find the joint density f(x, y).
b. The total effective life length of the two fuses is (X + Y). Find the expected total effective life length of a pair of fuses in a tele video computer terminal.