11.3 Exercise 32 — Applied Probability

(See Exercise 22 from "Problems On Random Vectors and Joint Distributions"). $f_{X Y} \left(t , u\right) = I_{\left[0 , 1\right]} \left(t\right) \frac{3}{8} \left(t^{2} + 2 u\right) + I_{\left(1 , 2\right]} \left(t\right) \frac{9}{14} t^{2} u^{2}$ ,

for $0 \leq u \leq 1$ .

f_{X} \left(t\right) = I_{\left[0 , 1\right]} \left(t\right) \frac{3}{8} \left(t^{2} + 1\right) + I_{\left(1 , 2\right]} \left(t\right) \frac{3}{14} t^{2} , f_{Y} \left(u\right) = \frac{1}{8} + \frac{3}{4} u + \frac{3}{2} u^{2} 0 \leq u \leq 1

Pfeiffer, Applied Probability, 11.3 Problems on Mathematical Expectation, exercise 32

AI Tutor