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

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.