11.3 Exercise 29 — Applied Probability

(See Exercise 19 from "Problems On Random Vectors and Joint Distributions"). $f_{X Y} \left(t , u\right) = \frac{12}{179} \left(3 t^{2} + u\right)$ , for $0 \leq t \leq 2$ , $0 \leq u \leq \min \left\{2 , 3 - t\right\}$ .

f_{X} \left(t\right) = I_{\left[0 , 1\right]} \left(t\right) \frac{24}{179} \left(3 t^{2} + 1\right) + I_{\left(1 , 2\right]} \left(t\right) \frac{6}{179} \left(9 - 6 t + 19 t^{2} - 6 t^{3}\right)

f_{Y} \left(u\right) = I_{\left[0 , 1\right]} \left(u\right) \frac{24}{179} \left(4 + u\right) + I_{\left(1 , 2\right]} \left(u\right) \frac{12}{179} \left(27 - 24 u + 8 u^{2} - u^{3}\right)

Pfeiffer, Applied Probability, 11.3 Problems on Mathematical Expectation, exercise 29

AI Tutor