The random variable X, the time to failure (in thousands ofmiles driven) of the signal lights on an automobile has a Weibulldistribution with a = 0.04 and ß = 2.
(a) Find the density, mean and variance for X.
(b) Find the reliability function for X.
(c) What is the reliability of these lights at 5,000 miles? At10,000 miles?
(d) What is the hazard rate function?
(e) What is the hazard rate at 5,000 miles? At 10,000 miles?
(f) What is the probability that the lights will fail during thefirst 3000 miles driven?