Let X denote the number of Canon digital cameras sold during a particular week by a certain store. The pmf of X is x | 01 2 3 4 pX(x) | .1 .2 .3 .25 .15 Sixty percent of all customers who purchase these cameras also buy an extended warranty. Let Y denote the number of purchasers during this week who buy an extended warranty.

a. What is P(X
4, Y
2)? [Hint: This probability equals P(Y
2⏐X
4)
P(X
4); now think of the four purchases as four trials of a binomial experiment, with success on a trial corresponding to buying an extended warranty.]

b. Calculate P(X
Y).

c. Determine the joint pmf of X and Y and then the marginal pmf of Y.