Let X denote the number of brand X VCRs sold during a particular week by a certain store. The pmf of X is x 0 1 2 3 4 .1 .2 .3 .25 .15 Seventy percent of all customers who purchase brand X VCRs 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.