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

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.