9.2 Exercise 21 — Applied Probability

The class $\left\{A , B , C , D , E , F\right\}$ is independent; the respective probabilites for these events are $\left\{0 . 46 , 0 . 27 , 0 . 33 , 0 . 47 , 0 . 37 , 0 . 41\right\}$ . Consider the simple random variables

X = 3 I_{A} - 9 I_{B} + 4 I_{C} , Y = - 2 I_{D} + 6 I_{E} + 2 I_{F} - 3 , \text{and} Z = 2 X - 3 Y

Determine $P \left(Y > X\right)$ , $P \left(Z > 0\right)$ , $P \left(5 \leq Z \leq 25\right)$ .

Pfeiffer, Applied Probability, 9.2 Problems on Independent Classes of Random Variables, exercise 21

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