The random variable X, the time to failure (in thousands of miles driven) of the signal lights on an automobile has a Weibull distribution with a = 0.04 and B = 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 5000 miles? 10,000 miles?
d) What is the hazard rate function?
e) What is the hazard rate function at 5000 miles? 10,000 miles?
f) What is the probability that the lights will fail during the first 3000 miles driven?