A room has two lamps that use bulbs of type A and B, respectively.The lifetime, X, of any particular bulb of a particular type is a random variable, independent of everything else, with the following PDF:
for type-A Bulbs: fX(x) =
e^−x, if x ≥ 0,
for type-B Bulbs: fX(x) =
3e^−3x, if x ≥ 0,
Both lamps are lit at time zero. Whenever a bulb is burned out it is immediately
replaced by a new bulb.
(a) What is the expected value of the number of type-B bulb failures until time t?
The time is infinity? how is this possible?
(b) What is the PDF of the time until the first failure of either bulb type?
lamdatotal = lamda 1 + lamda2
(c) Find the expected value and variance of the time until the third failure of a
(d) Suppose that a type-A bulb has just failed. How long do we expect to wait until a subsequent type-B bulb failure?