The lifetime (in months) of two components in a certain device are random variables X and Y that have joint probability distribution function 9216 (48 – 2x – y) if x 2 0, y 2 0, 2x +y < 48 p(x, y) = otherwise Calculate the probability that both components function for at least 12 months without failing. Note that p(x, y) is nonzero only within the tri- angle bounded by the coordinate axes and the line 2x + y = 48 shown in Figure у (months) 48 2x + y = 48 36 Region where x2 12, y 2 12 and 2x + y 5 48 24 + 12 →x (months) 12 24 FIGURE

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