In the article “Parameter Estimation with Only One Complete Failure Observation” (W. Pang, P. Leung, et al., International Journal of Reliability, Quality, and Safety Engineering, 2001:109–122), the lifetime, in hours, of a certain type of bearing is modeled with the Weibull distribution with parameters α = 2.25 and β = 4.474 × 10−4.

a. Find the probability that a bearing lasts more than 1000 hours.

b. Find the probability that a bearing lasts less than 2000 hours.

c. Find the median lifetime of a bearing.

d. The hazard function is defined in Exercise 8. What is the hazard at t = 2000 hours?