Given the following Bayesian Network consisting of four Bernoulli random variables and the associated conditional probability tables :
P(.) U = 0 0.5 U = 1 0.5
P(V = 0| .) P(V = 1| .) U = 0 0.5 0.5 U = 1 0.5 0.5 P(W = 0| .) P(W = 1| .) U = 0 1 0 U = 1 0 1
P(Z = 0| .) P(Z = 1| .) V = 0 W = 0 0.5 0.5 V = 0 W = 1 1 0 V = 1 W = 0 1 0 V = 1 W = 1 0.5 0.5
The value of P(U = 1, V = 1, W = 1,Z= 1) = ______. (rounded off to three decimal places)
| P(.) | |
| U = 0 | 0.5 |
| U = 1 | 0.5 |
| P(V = 0| .) | P(V = 1| .) | |
| U = 0 | 0.5 | 0.5 |
| U = 1 | 0.5 | 0.5 |
| P(W = 0| .) | P(W = 1| .) | |
| U = 0 | 1 | 0 |
| U = 1 | 0 | 1 |
| P(Z = 0| .) | P(Z = 1| .) | ||
| V = 0 | W = 0 | 0.5 | 0.5 |
| V = 0 | W = 1 | 1 | 0 |
| V = 1 | W = 0 | 1 | 0 |
| V = 1 | W = 1 | 0.5 | 0.5 |
Correct Answer: 0.125
Solution and Explanation
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