11.3 Exercise 27 — Applied Probability

(See Exercise 17 from "Problems On Random Vectors and Joint Distributions"). $f_{X Y} \left(t , u\right) = \frac{24}{11} t u$ for $0 \leq t \leq 2$ , $0 \leq u \leq \min \left\{1 , 2 - t\right\}$ .

f_{X} \left(t\right) = I_{\left[0 , 1\right]} \left(t\right) \frac{12}{11} t + I_{\left(1 , 2\right]} \left(t\right) \frac{12}{11} t \left(2 - t\right)^{2} , f_{Y} \left(u\right) = \frac{12}{11} u \left(u - 2\right)^{2} , 0 \leq u \leq 1

Pfeiffer, Applied Probability, 11.3 Problems on Mathematical Expectation, exercise 27

AI Tutor