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11.3 Exercise 37

Avg difficulty 2.5

fXY(t,u)=388(2t+3u2)f_{X Y} \left(t , u\right) = \frac{3}{88} \left(2 t + 3 u^{2}\right) for 0≤t≤20 \leq t \leq 2, 0≤u≤1+t0 \leq u \leq 1 + t (see the exercise).

Z = I [ 0 , 1 ] ( X ) 4 X + I ( 1 , 2 ] ( X ) ( X + Y ) 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, 11.3 Problems on Mathematical Expectation, exercise 37

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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.