14.2 Exercise 15 — Applied Probability

$f_{X Y} \left(t , u\right) = \frac{2}{13} \left(t + 2 u\right)$ , for $0 \leq t \leq 2$ , $0 \leq u \leq \min \left\{2 t , 3 - t\right\}$ . (see Exercise 31 from "Problems on Mathematical Expectation", and the exercise).

f_{X} \left(t\right) = I_{\left[0 , 1\right]} \left(t\right) \frac{12}{13} t^{2} + I_{\left(1 , 2\right]} \left(t\right) \frac{6}{13} \left(3 - t\right)

Z = I_{M} \left(X , Y\right) \left(X + Y\right) + I_{M^{c}} \left(X , Y\right) 2 Y^{2} , M = \left\{\left(t , u\right) : t \leq 1 , u \geq 1\right\}

Pfeiffer, Applied Probability, 14.2 Problems on Conditional Expectation, Regression, exercise 15

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