X is a continuous uniform (a, a + ) random variable, and Y is a continuous uniform (b, b + )

random variables, where > 0,> 0, and a, b R.

(a) (2 marks) Find all possible pairs of numbers (, ) for which X and Y are independent.

(b) (3 marks) If X and Y are independent, describe the region

R = {(x, y) R^2| fX,Y (x, y) > 0}

geometrically. Justify your answer.