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In Exercise 5.16, Y1 and Y2 denoted the proportions of time that employees I and II actually spent working on their assigned tasks during a workday. The joint density of Y1 and Y2 is given by
In Exercise 5.80, we derived the mean of the productivity measure 30Y1 + 25Y2. Find the variance of this measure of productivity. Give an interval in which you think the total productivity measures of the two employees should lie for at least 75% of the days in question.
5.16 Let Y1 and Y2 denote the proportions of time (out of one workday) during which employees I and II, respectively, perform their assigned tasks. The joint relative frequency behavior of Y1 and Y2 is modeled by the density
a Find P(Y1 < 1/2, Y2 > 1/4).
b Find P(Y1 + Y2 ≤ 1).
5.80 In Exercise 5.16, Y1 and Y2 denoted the proportions of time that employees I and II actually spent working on their assigned tasks during a workday. The joint density of Y1 and Y2 is given by
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
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Chapter 5 Solutions
Mathematical Statistics with Applications
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