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Multivariate Probability Distributions

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Y1 & Y2 denotes the proportions of time that employee I and II actually spent working on their assigned tasks during a workday. The joint density of Y1 & Y2 is given by:

f(y1,y2) = y1 + y2 , 0=<y1=<1 , 0=<y2=<1
f(y1,y2) = 0, elsewhere

Employee I has a higher productivity rating than employee II, and a measure of the total productivity of the pair of employees is 30Y1 + 25Y2 . Find the expected value of this measure of productivity.

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Productivity is calculated based on joint probability density. The solution is detailed and well presented.

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