4.22

a. A very large shipment of parts contains 10% defectives.

Two parts are chosen at random from the shipment and checked. Let the random variable X denote the number of defectives found.

Find the probability distribution of this random variable.

b. A shipment of 20 parts contains 2 defectives. Two parts are chosen at random from the shipment and checked. Let the random variable Y denote the number of defectives found. Find the probability distribution of this random variable. Explain why your answer is different from that for part (a).

c. Find the mean and variance of the random variable X in part (a).

d. Find the mean and variance of the random variable Y in part (b).