Let X denote the number of Canon digital cameras sold during a particular week by a cert...

Let X denote the number of Canon digital cameras sold during a particular week by a certain store. The pmf of X is

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.