Please see the attached file for full problem description.
a) A lamp has two bulbs of a type with an average lifetime of 1000 hours. Assuming that we can model the probbility of failure of these bulbs by an exponential density function with mean mu = 1000. Find the probability that both of the bulbs fail in 1000 hours.
b) Another lamp has one bulb of the same type. If it burns out , it is replaced with another. Find the probability that both fail within a total of 1000 hours.
Probabilities are calculated using an exponential density function.