A firm is contemplating the purchase of 500 printer cartridges. One supplier, supplier A, offers the cartridges at $15 each, guarantees each cartridge, and will replace all defective cartridges free. A second supplier, supplier B, offers the cartridges at $14 each with no guarantee. However, supplier B will replace defective cartridges with good cartridges for $10 per cartridge. Suppose that the proportion of defective cartridges produced by supplier B is denoted by , and suppose that the prior distribution for is a beta distribution with parameters = 2 and = 50.

(a) (5 points) What should the firm do on the basis of the prior distribution?

(b) (10 points) How much is it worth to the firm to know the proportion of defective cartridges for certain?

(c) (10 points) Suppose that supplier B can provide a randomly chosen sample of 10 cartridges. What is the value of information provided by this sample?

(d) (10 points) In the sample of 10 cartridges, 1 is defective. Find the posterior distribution of and use this distribution to determine which supplier the firm should deal with.

1A rm is contemplating the purchase of 500 printer cartridges. One supplier, supplier A, offers the cartridges at $15 each, guarantees each cartridge, and will replace all defective cartridges free. A second supplier, supplier B, offers the cartridges at $14 each with no guarantee. However, supplier B will replace defective cartridges with good cartridges for $10 per cartridge. Suppose that the proportion of defective cartridges produced by supplier B is denoted by p, and suppose that the prior distribution for p is a beta distribution with parameters I" = 2 and '1' = 50. (a) (5 points) What should the rm do on the basis of the prior distribution? (b) (10 points) How much is it worth to the firm to know the proportion of defective cartridges for certain? (c) (10 points) Suppose that supplier B can provide a randomly chosen sample of 10 cartridges. What is the value of information provided by this sample? (d) (10 points) In the sample of 10 cartridges, 1 is defective. Find the posterior distribution gm and use this distribution to determine which supplier the rm should deal with