After 10 years of life, a certain type of flexible hose used in Naval ships has a Weibull (Beta, eta) lifetime distribution (life is measured in years). The life is considered from the time the hose has been fitted to the time when it was replaced.

Let X denote the life time of hose beyond the initial 10 years.

Let Beta = 2.8, eta = 8.6, and t = 2.4.

a) What is the mean life time of a hose beyond the initial 10 years (2dp). :

Do not use units.

b) Evaluate P(X<=eta) (3dp). :

Where <= means less than or equal to.

c) Suppose m is such that P(X<=m) = 1/2. What is the value of m (3 dp)? :

d) What is the value of the hazard rate h(t) (3 dp)? :