Question

2.2 Noisy-OR (a) Conditional probability table Complete the noisy-OR conditional probability table for the belief network shown above. (The missing values in the table are determined by the ones shown.) X1 | X2 | X3 | P(Y = 1|X1, X2, X3) ---|---|---|--- 0 | 0 | 0 | 0 1 | 0 | 0 | 0 | 1 | 0 | 1/3 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 4/5 1 | 1 | 1 | 5/6 (b) Qualitative reasoning Suppose that each node Xi in this model has some finite, non-zero prior probability to be either zero or one; namely 0 < P(Xi = 1) < 1. Sort the following probabilities from smallest to largest: P(X2 = 1) P(X2 = 1|Y = 0) P(X2 = 1|Y = 1) P(X2 = 1|Y = 1, X1 = 0, X3 = 0) P(X2 = 1|Y = 1, X1 = 1, X3 = 1) For this part, you are not required to compute numerical values for these probabilities, only to sort them in ascending order. In fact, this part can be completed independently of the values in part (a). (c) Quantitative reasoning Suppose that P(Xi = 1) = 1/3 for i in {1, 2, 3}. Compute numerical values for the probabilities in part (b) from these priors and your answers in part (a). Do these values match your previous ordering?

          2.2 Noisy-OR
(a) Conditional probability table
Complete the noisy-OR conditional probability table for the belief network shown above. (The missing values in the table are determined by the ones shown.)

X1 | X2 | X3 | P(Y = 1|X1, X2, X3)
---|---|---|---
0 | 0 | 0 | 0
1 | 0 | 0 | 
0 | 1 | 0 | 1/3
0 | 0 | 1 | 
1 | 1 | 0 | 
1 | 0 | 1 | 
0 | 1 | 1 | 4/5
1 | 1 | 1 | 5/6

(b) Qualitative reasoning
Suppose that each node Xi in this model has some finite, non-zero prior probability to be either zero or one; namely 0 < P(Xi = 1) < 1. Sort the following probabilities from smallest to largest:
P(X2 = 1)
P(X2 = 1|Y = 0)
P(X2 = 1|Y = 1)
P(X2 = 1|Y = 1, X1 = 0, X3 = 0)
P(X2 = 1|Y = 1, X1 = 1, X3 = 1)
For this part, you are not required to compute numerical values for these probabilities, only to sort them in ascending order. In fact, this part can be completed independently of the values in part (a).
(c) Quantitative reasoning
Suppose that P(Xi = 1) = 1/3 for i in {1, 2, 3}. Compute numerical values for the probabilities in part (b) from these priors and your answers in part (a). Do these values match your previous ordering?

2.2 Noisy-OR
(a) Conditional probability table
Complete the noisy-OR conditional probability table for the belief network shown above. (The missing values in the table are determined by the ones shown.)

X1 | X2 | X3 | P(Y = 1|X1, X2, X3)
—|—|—|—
0 | 0 | 0 | 0
1 | 0 | 0 |
0 | 1 | 0 | 1/3
0 | 0 | 1 |
1 | 1 | 0 |
1 | 0 | 1 |
0 | 1 | 1 | 4/5
1 | 1 | 1 | 5/6

(b) Qualitative reasoning
Suppose that each node Xi in this model has some finite, non-zero prior probability to be either zero or one; namely 0 < P(Xi = 1) < 1. Sort the following probabilities from smallest to largest:
P(X2 = 1)
P(X2 = 1|Y = 0)
P(X2 = 1|Y = 1)
P(X2 = 1|Y = 1, X1 = 0, X3 = 0)
P(X2 = 1|Y = 1, X1 = 1, X3 = 1)
For this part, you are not required to compute numerical values for these probabilities, only to sort them in ascending order. In fact, this part can be completed independently of the values in part (a).
(c) Quantitative reasoning
Suppose that P(Xi = 1) = 1/3 for i in 1, 2, 3. Compute numerical values for the probabilities in part (b) from these priors and your answers in part (a). Do these values match your previous ordering?

Added by Taylor A.

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