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11.3 Exercise 21

Avg difficulty 2.5

(See Exercise 11 from "Problems On Random Vectors and Joint Distributions"). $f_{X Y} \left(t , u\right) = 1 / 2$ on the square with vertices at $\left(1 , 0\right) , \left(2 , 1\right) , \left(1 , 2\right) , \left(0 , 1\right)$ .

f_{X} \left(t\right) = f_{Y} \left(t\right) = I_{\left[0 , 1\right]} \left(t\right) t + I_{\left(1 , 2\right]} \left(t\right) \left(2 - t\right)

Pfeiffer, Applied Probability, 11.3 Problems on Mathematical Expectation, exercise 21

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