AI Tutor
Back to 11.3 Problems on Mathematical Expectation

11.3 Exercise 41

Avg difficulty 2.5

fXY(t,u)=12227(3t+2tu)f_{X Y} \left(t , u\right) = \frac{12}{227} \left(3 t + 2 t u\right), for 0≤t≤20 \leq t \leq 2, 0≤u≤min{1+t,2}0 \leq u \leq \min \left\{1 + t , 2\right\} (see the exercise).

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

Pfeiffer, Applied Probability, 11.3 Problems on Mathematical Expectation, exercise 41

AI Tutor

Adapted from Applied Probability © 2009 Paul E. Pfeiffer. Licensed under CC BY 3.0. Source: Applied Probability. Imported at revision d7a0420.