A privately owned liquor store operates both a drive-in facility and a walk-in facility.

On a randomly selected day, let X and Y, respectively, be the proportions of the time that the drive-in and walk-in facilities are in use, and suppose that the joint density function of these variables is

\(f(x,y)=\begin{cases}\frac{2}{3}(x+2y) & 0\leq1.0\leq y\leq1\\ 0, & elsewhere\end{cases}\)

0, elsewhere.

a. Find the marginal density of X.

b. Find the marginal density of Y.

c. Find the probability that the drive-in facility is busy less than one-half of the time.