Suppose that a point (X, Y) is chosen at random from the rectangle S defined as follows:

Question:

Suppose that a point (X, Y) is chosen at random from the rectangle S defined as follows:
S = {(x, y) : 0 ≤ x ≤ 2 and 1≤ y ≤ 4}.
a. Determine the joint p.d.f. of X and Y, the marginal p.d.f. of X, and the marginal p.d.f. of Y.
b. Are X and Y independent?