Two production lines are used to pack sugar into 5 kg bags. Line 1 produces twice as many bags as does line 2. One percent of the bags from line 1 are defective in that they fail to meet a purity specification, c. Show that the marginal density of Y is fY (y) = 1/(d − c) for c < y < d. d. Use parts (a), (b), and (c) to show that X and Y are independent. while 3% of the bags from line 2 are defective. A bag is randomly chosen for inspection.

a. What is the probability that it came from line 1?

b. What is the probability that it is defective?

c. If the bag is defective, what is the probability that it came from line 1?

d. If the bag is not defective, what is the probability that it came from line 1?