The failure distribution f(t) is given as:
f(t) = 0, for 0 ≤ t ≤ 1000 hours
(a) The probability of failure within the 100-hour warranty period is given by the cumulative distribution function (CDF) of the failure distribution up to 100 hours:
F(100) = ∫[0,100] f(t) dt = ∫[0,100] 0 dt = 0
Therefore, the probability of failure within the 100-hour warranty period is 0.
(b) The mean time to failure (MTTF) is given by the expected value of the failure distribution:
MTTF = ∫[0,1000] t f(t) dt
Since the failure distribution is 0 for all values of t, the MTTF is also 0. This means that the expected value of the time until failure is 0, which implies that the failure occurs immediately with probability 1.
