4. (25 pts) Consider the function fx, y (2, y) = Jcay 0

4. (25 pts) Consider the function cry 0 1 where c is a constant. otherwise a. Compute c so that fx Y(x, y) is a probability density function. b. Compute the marginal probability density functions fx and fy, mean- ing fx(x) fx Y (x, y)dy and fy (y) fx Y (x, y)dx. c. Are the random variables X and Y independent, meaning is it true that fx Y(x, y) = for all x and y?