The Acme Super light bulb is known to have a useful life described by the density function

[[math]] f(t) = .01e^{-.01t}\ , [[/math]]

where time [math]t[/math] is measured in hours.

• Find the failure rate of this bulb (see exercise).
• Find the reliability of this bulb after 20 hours.
• Given that it lasts 20 hours, find the probability that the bulb lasts another 20 hours.
• Find the probability that the bulb burns out in the forty-first hour, given that it lasts 40 hours.