7.4 An environmental engineer measures the amount (by weight) of particulate pollution in air samples (of a
Question:
7.4 An environmental engineer measures the amount
(by weight) of particulate pollution in air samples (of a certain volume) collected over the smokestack of a coal-operated power plant. Let X1 denote the amount of pollutant per sample when a certain cleaning device on the stack is not operating, and let X2 denote the amount of pollutant per sample when the cleaning device is operating, under similar environmental conditions. It is observed that X1 is always greater than 2X2, and the relative frequency behavior of (X1, X2) can be modeled by Jk 0x2, 0x21, 2x2 = x f(x1, x2)= 10 elsewhere:
(That is, X1 and X2 are randomly distributed over the region inside the triangle bounded by a Find the value of k that makes this a probability density function. b Find . (That is, find the probability that the cleaning device will reduce the amount of pollutant by one-third or more.)
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