14.2 Exercise 12 — Applied Probability

$f_{X Y} \left(t , u\right) = \frac{3}{88} \left(2 t + 3 u^{2}\right)$ for $0 \leq t \leq 2$ , $0 \leq u \leq 1 + t$ (see Exercise 37 from "Problems on Mathematical Expectation", and the exercise).

f_{X} \left(t\right) = \frac{3}{88} \left(1 + t\right) \left(1 + 4 t + t^{2}\right) = \frac{3}{88} \left(1 + 5 t + 5 t^{2} + t^{3}\right) , 0 \leq t \leq 2

Z = I_{\left[0 , 1\right]} \left(X\right) 4 X + I_{\left(1 , 2\right]} \left(X\right) \left(X + Y\right)

Pfeiffer, Applied Probability, 14.2 Problems on Conditional Expectation, Regression, exercise 12

AI Tutor