Maurice Tutor

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    Argosy University/ Phoniex University/
    Nov-2005 - Oct-2011

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    Phoniex University
    Oct-2001 - Nov-2016

Category > Management Posted 30 Jan 2018 My Price 9.00

joint distribution of amount

The joint distribution of amount of pollutant emitted from a smokestack without a cleaning device (Y1) and a similar smokestack with a cleaning device (Y2) was given in Exercise 5.10 to be

The reduction in amount of pollutant due to the cleaning device is given by U = Y1 − Y2.

a Find the probability density function for U.

b Use the answer in part (a) to find E(U). Compare your results with those of Exercise 5.78(c).

Exercise 5.10

An environmental engineer measures the amount (by weight) of particulate pollution in air samples of a certain volume collected over two smokestacks at a coal-operated power plant. One of the stacks is equipped with a cleaning device. Let Y1 denote the amount of pollutant per sample collected above the stack that has no cleaning device and let Y2 denote the amount of pollutant per sample collected above the stack that is equipped with the cleaning device.

Suppose that the relative frequency behavior of Y1 and Y2 can be modeled by

That is, Y1 and Y2 are uniformly distributed over the region inside the triangle bounded by y1 = 2, y2 = 0, and 2y2 = y1.

a Find the value of k that makes this function a probability density function.

b Find P(Y1 ≥ 3Y2). That is, find the probability that the cleaning device reduces the amount of pollutant by one-third or more.

Exercise 5.78(c)

c The random variable Y1 − Y2 represents the amount by which the weight of pollutant can be reduced by using the cleaning device. Find E(Y1 − Y2).

d Find V(Y1 − Y2). Within what limits would you expect Y1 − Y2 to fall?

 

Answers

Maurice Tutor
(5)
Status NEW Posted 30 Jan 2018 11:01 PM My Price 9.00

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