6. Consider the context of Example 3.3-9 where there is a cost associated with either early (i.e., before 15 days)

or late (i.e., after 15 days) completion of the project. In an effort to reduce the cost, the company plans to start working on the project five days after the project is commissioned.

Thus, the cost due to early or late completion of the project is given by (Y = h((T ), where (T = T + 5, and the function h is h(˜t) = 5(15 − ˜t) if ˜t < 15, and h(˜t) = 10(˜t−15) if ˜t > 15. The PDF of T is fT(t) = 0.1 exp(−0.1t)

for t > 0, and 0 otherwise.

(a) Find the PDF of f(T (˜t) of(T. (Hint. First find the CDF F(T (˜t) of(T .)

(b) Use R commands similar to those given in Example 3.3-9 to find the expected cost, E((T ). Does the company’s plan to delay the work on the project reduce the expected cost?