Let X and Y be two random variables with joint density function f(x,y) = (3 − x + 2y) / 60, for 1 < x < 3, 0 < y < 5. Is P(X > 2, Y < 3) equal to P(X > 2) × P(Y < 3)?

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Let X and Y be two random variables with joint density function

f(x,y) = (3 − x + 2y) / 60, for 1 < x < 3, 0 < y < 5.

Is P(X > 2, Y < 3) equal to P(X > 2) × P(Y < 3)?

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