11.3 Exercise 28 — Applied Probability

(See Exercise 18 from "Problems On Random Vectors and Joint Distributions"). $f_{X Y} \left(t , u\right) = \frac{3}{23} \left(t + 2 u\right)$ for $0 \leq t \leq 2$ , $0 \leq u \leq \max \left\{2 - t , t\right\}$ .

f_{X} \left(t\right) = I_{\left[0 , 1\right]} \left(t\right) \frac{6}{23} \left(2 - t\right) + I_{\left(1 , 2\right]} \left(t\right) \frac{6}{23} t^{2} , f_{Y} \left(u\right) = I_{\left[0 , 1\right]} \left(u\right) \frac{6}{23} \left(2 u + 1\right) + I_{\left(1 , 2\right]} \left(u\right) \frac{3}{23} \left(4 + 6 u - 4 u^{2}\right)

Pfeiffer, Applied Probability, 11.3 Problems on Mathematical Expectation, exercise 28

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