11.3 Exercise 25 — Applied Probability

(See Exercise 15 from "Problems On Random Vectors and Joint Distributions"). $f_{X Y} \left(t , u\right) = \frac{3}{88} \left(2 t + 3 u^{2}\right)$ for $0 \leq t \leq 2$ , $0 \leq u \leq 1 + t$ .

f_{X} \left(t\right) = \frac{3}{88} \left(1 + t\right) \left(1 + 4 t + t^{2}\right) = \frac{3}{88} \left(1 + 5 t + 5 t^{2} + t^{3}\right) , 0 \leq t \leq 2

f_{Y} \left(u\right) = I_{\left[0 , 1\right]} \left(u\right) \frac{3}{88} \left(6 u^{2} + 4\right) + I_{\left(1 , 3\right]} \left(u\right) \frac{3}{88} \left(3 + 2 u + 8 u^{2} - 3 u^{3}\right)

Pfeiffer, Applied Probability, 11.3 Problems on Mathematical Expectation, exercise 25

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