Please see the attached file for the fully formatted problems.
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.
Productivity is calculated based on joint probability density. The solution is detailed and well presented.