Refer to Exercise 4.11, where Y is the number of firing pins tested in a sample of five selected from a large lot. Suppose the cost of inspecting a single pin is $300 if the pin is defective and $100 if not. Then the total cost C (in dollars) of the inspection is given by the equation C = 200 + 100Y. Find the mean and variance of C.

Data from Exercise 4.11

A quality control engineer samples five from a large lot of manufactured firing pins and checks for defects. Unknown to the inspector, three of the five sampled firing pins are defective. The engineer will test the five pins in a randomly selected order until a defective is observed (in which case the entire lot will be rejected). Let Y be the number of firing pins the quality control engineer must test.