Answer Happy

Let Yį and Y, denote the proportions of time (out of one workday) during which employees I and II, respectively, perform their assigned tasks. The joint relative frequency behaviour of Y, and Y2 is modelled by the density function = 0 < y1 = 1,0 < y2 S1, elsewhere. 0 fU»Y) = {Party? 2. Y>>. (2) 1.1.1. Find P(Y_< ={* * : 1.1.2. The marginal density function of Y2 is 1 f2(y2) = + 2 0 < y2 <1, 0, elsewhere. Find the marginal density function of Y. (2.5) 1.1.3. If employee II spends exactly 50% of the day working on assigned duties, find the probability that employee I spends more than 75% of the day working on similar duties. (2) 1.1.4. Are Y, and Y2 independent [State the reason for your answer]? (1) 1.1.5. 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.(2.5)

Let Yį and Y, denote the proportions of time (out of one workday) during which employees I and II, respectively, perform their assigned tasks. The joint relative frequency behaviour of Y, and Y2 is modelled by the density function = 0 < y1 = 1,0 < y2 S1, elsewhere. 0 fU»Y) = {Party? 2. Y>>. (2) 1.1.1. Find P(Y_< ={* * : 1.1.2. The marginal density function of Y2 is 1 f2(y2) = + 2 0 < y2 <1, 0, elsewhere. Find the marginal density function of Y. (2.5) 1.1.3. If employee II spends exactly 50% of the day working on assigned duties, find the probability that employee I spends more than 75% of the day working on similar duties. (2) 1.1.4. Are Y, and Y2 independent [State the reason for your answer]? (1) 1.1.5. 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.(2.5)