11.3 Exercise 26 — Applied Probability

(See Exercise 16 from "Problems On Random Vectors and Joint Distributions"). $f_{X Y} \left(t , u\right) = 12 t^{2} u$ on the parallelogram with vertices

\left(- 1 , 0\right) , \left(0 , 0\right) , \left(1 , 1\right) , \left(0 , 1\right)

f_{X} \left(t\right) = I_{\left[- 1 , 0\right]} \left(t\right) 6 t^{2} \left(t + 1\right)^{2} + I_{\left(0 , 1\right]} \left(t\right) 6 t^{2} \left(1 - t^{2}\right) , f_{Y} \left(u\right) = 12 u^{3} - 12 u^{2} + 4 u , 0 \leq u \leq 1

Pfeiffer, Applied Probability, 11.3 Problems on Mathematical Expectation, exercise 26

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