139. A component has lifetime X that is exponentially distributed with parameter l.

a. If the cost of operation per unit time is

c, what is the expected cost of operating this component over its lifetime?

b. Instead of a constant cost rate c as in part (a), suppose the cost rate is c(1  .5eax) with a  0, so that the cost per unit time is less than c when the component is new and gets more expensive as the component ages. Now compute the expected cost of operation over the lifetime of the component.