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11.3 Exercise 39

Avg difficulty 2.5

fXY(t,u)=323(t+2u)f_{X Y} \left(t , u\right) = \frac{3}{23} \left(t + 2 u\right) for 0≤t≤20 \leq t \leq 2, 0≤u≤max{2-t,t}0 \leq u \leq \max \left\{2 - t , t\right\} (see the exercise).

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

Pfeiffer, Applied Probability, 11.3 Problems on Mathematical Expectation, exercise 39

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