6. Let X denote the number of Canon digital cameras sold during a particular week by a certain store. The pmf of X is x 0 1 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 ; 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.

P1Y  2 0 X  42 # P1X  42