The weekly number of MACs and PCs sold by a salesperson at the local computer store can be represented as the outcome of a bivariate random variable \((X, Y)\) with the nonzero values of its joint probability density function given by the following table of probabilities:

( \(\mathrm{X}\) is the number of MACs and \(\mathrm{Y}\) is the number of PCs). The salesperson receives a salary of \(\$ 200 /\) week, and also receives a commission of \(\$ 50\) for every MAC sold and \(\$ 100\) for every PC sold.

(a) What is the expected value of the weekly commission that the salesperson obtains from selling computers? What is the expected value of her total pay received from selling computers?

(b) What is the expected value of her commission from selling MACs? What is the expected value of her commission from selling PCs?

(c) Given that the salesperson sells three PCs, what is the expected value of her commission from selling MACs?

(d) If 40 percent of the salesperson's total pay is deducted for federal and state taxes, what is the expected value of her pay after taxes?

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