Question

The employees of a firm that does asbestos cleanup are being tested for indications of asbestos in their lungs. The firm is asked to send four employees who have positive indications of asbestos to a medical center for further testing. Suppose 40% of the population have positive indications of asbestosin their lungs. Let X be the number of employees who do not have asbestosin their lungs tested before finding four who do have asbestos in their lungs.

(a) (2 points) What is the probability distribution of X? Write down thedistribution family and the parameter(s).

(b) (2 points) Let Y be the total number of employees tested when finding four with positive asbestos in their lungs. Express Y as a function of X.

(c) (4 points) Find the pmf ofY.

(d) (4 points) Suppose the cost to set up the test is $300, and each testcosts $40. Define the total cost of the tests when finding four with positive asbestos in their lungs as Z. Express Z as a function of X.

(e) (4 points) Calculate the expected value of Z.

Answer 1