Mathematics, 30.11.2020 18:30 nyaa70
Let Y1 and Y2 denote the proportion of time during which employees I and II actually performed their assigned tasks during a workday, The joint density of Y1 and Y2 is given by
f(y1,y2) = { y1+y2, 0<=y1<=1, 0<=y2<=1, 0, elsewhere
Required:
a. Find the marginal density function of Y1 and Y2
b. Find P(Y1 >= 1/2 | Y2 >= 1/2).
c. If employee II spends exactly 50% of the dayworking on assigned duties, find the probability that employee I spends more than 75% of the day working on similarduties.
Answers: 2
and 
is given by:
![= y_1[y_2]^1_0 + \bigg [ \dfrac{y_2^2}{2}\bigg]^1_0](/tpl/images/0934/0820/510d0.png)
![= y_1 [1] + [\dfrac{1}{2}]](/tpl/images/0934/0820/12df5.png)
![=\bigg[ \dfrac{y_1^2}{2} \bigg]^1_0 + y_2 [y_1]^1_0](/tpl/images/0934/0820/51f1e.png)
![= [ \dfrac{1}{2}] + y_2 [1]](/tpl/images/0934/0820/dfe7b.png)
![P\bigg[y_1 \ge \dfrac{1}{2}\bigg |y_2 \ge \dfrac{1}{2} \bigg] = \dfrac{P\bigg [y_1 \ge \dfrac{1}{2} . y_2 \ge\dfrac{1}{2} \bigg]}{P\bigg[ y_2 \ge \dfrac{1}{2}\bigg]}](/tpl/images/0934/0820/fb2b5.png)
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Let Y1 and Y2 denote the proportion of time during which employees I and II actually performed their...
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