A student budgets $60 weekly for gas and a few quick meals off-campus. Let X denote the amount spent for gas and Y the amount spent for quick meals in a typical week. Assume this student is very disciplined and sticks to the budget, spending $60 on these two things each week.
(a) Can we model X and Y as independent random variables? Explain.
(b) Suppose we assume X and Y are dependent. What is the effect of this dependence on the variance of X + Y?