In the textbook Exercise 5.10, we had to show that 1, 0< yı < 2, 0 < y2 < 1, 2y2 < yı, 0, elsewhere fV1, y2) = is a valid joint probability density function for Y1, the amount of pollutant per sample collected above the stack without the cleaning device, and Y2, the amount collected above the stack with the cleaner. Find E(Y1) and E(Y2). Find V(Y1) and V(Y2). The random variable Y1- Y2 represents the amount by which the weight of pollutant can be reduced by using the cleaning device. Find E(Y¡ – Y2).

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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In the textbook Exercise 5.10, we had to show that
1, 0s y < 2, 0< y2 < 1, 2y2 < yı,
f(V1, y2) =
%3D
0, elsewhere
is a valid joint probability density function for Y1, the amount of pollutant per sample collected above
the stack without the cleaning device, and Y2, the amount collected above the stack with the cleaner.
Find E(Y1) and E(Y2).
Find V(Y1) and V(Y2).
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).
Transcribed Image Text:In the textbook Exercise 5.10, we had to show that 1, 0s y < 2, 0< y2 < 1, 2y2 < yı, f(V1, y2) = %3D 0, elsewhere is a valid joint probability density function for Y1, the amount of pollutant per sample collected above the stack without the cleaning device, and Y2, the amount collected above the stack with the cleaner. Find E(Y1) and E(Y2). Find V(Y1) and V(Y2). 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).
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Just calculate the marginal density at first then calculate expectation and variance.............

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