If X is the amount of money (in dollars) that a salesperson spends on gasoline during a day and Y is the corresponding amount of money (in dollars) for which he or she is reimbursed, the joint density of these two random variables is given by
![](https://test.transtutors.com/qimg/d8363261-1dcb-4b36-a006-88d25b168ee3.png)
find
(a) the marginal density of X;
(b) the conditional density of Y given X = 12;
(c) the probability that the salesperson will be reimbursed at least $8 when spending $12.