Midterm-4) (30 points) A service facility operates with two service lines. On a randomly selected day, let X be the proportion of time that the first line is in use whereas Y is the proportion of time that the second line is in use. Suppose that the joint probability density function for (X, Y) is (x + y, f(x) = 0, 0 ≤ x, y ≤ 1 elsewhere. A) Determine whether or not X and Y are independent. (10 points) B) Find Var(X+Y). (20 points)

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