chemical solution, and the random variable Ymeasures the acidity of the solution. They have a joint probability density function f(x, y) = A(20-x-2y) for 0 ≤ x ≤ 5 and 0 ≤ y = 5, and f(x, y) = 0 elsewhere. (a) What is the value of A? (b) What is P(1 ≤ X ≤ 2, 2 ≤ Y≤ 3)? (c) Construct the marginal probability density functions fx(x) and fy(y). (d) Are the ethanol concentration and the acidity independent?

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