10.4 Exercise 16 — Applied Probability

The class $\left\{X , Y , Z\right\}$ is independent.

$X = - 2 I_{A} + I_{B} + 3 I_{C}$ . Minterm probabilities are (in the usual order)

0 . 255 0 . 025 0 . 375 0 . 045 0 . 108 0 . 012 0 . 162 0 . 018

$Y = I_{D} + 3 I_{E} + I_{F} - 3$ . The class $\left\{D , E , F\right\}$ is independent with

P \left(D\right) = 0 . 32 P \left(E\right) = 0 . 56 P \left(F\right) = 0 . 40

Z has distribution

Value	-1.3	1.2	2.7	3.4	5.8
Probability	0.12	0.24	0.43	0.13	0.08

Determine $P \left(X^{2} + 3 X Y^{2} > 3 Z\right)$ .

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