Question

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
P(Y = 2 I 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.