Let X Denote the Number of Brand X VCRs Sold

Let X denote the number of brand X VCRs sold during a particular week by a certain store. The pmf of X is $$\begin{array}{l}\begin{array} { l l l l l l } \hline x & 0 & 1 & 2 & 3 & 4 \\\hline & .1 & .2 & .3 & .25 & .15\end{array}\\p _ { x } ( x )\\\hline\end{array}$$ 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) $\text { . }$
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.