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11.3 Exercise 36

Avg difficulty 2.5

For the pair {X,Y}\left\{X , Y\right\} in the exercise, let

W = g X , Y ) = X for X + Y ≤ 4 2 Y for X + Y > 4 = I M ( X , Y ) X + I M c ( X , Y ) 2 Y W = g X , Y \left.\right) = \left\{\begin{matrix} X & \text{for} X + Y \leq 4 \\ 2 Y & \text{for} X + Y > 4 \end{matrix}\right = I_{M} \left(X , Y\right) X + I_{M^{c}} \left(X , Y\right) 2 Y

Determine E[W]E \left[W\right] and E[W2]E \left[W^{2}\right].

Pfeiffer, Applied Probability, 11.3 Problems on Mathematical Expectation, exercise 36

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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.