Homework VII-KEY1. A graph with no links is a trivial D-Map. True/FalseTrue. A graph is said to be D- Map of a distribution if all CI satisfied by distribution is reflected onthe graph, of course graph with no links will reflect any conditional independency.2. Consider the Bayesian network given belowa. Is A conditionally independent of D give {B,C}.Yes,b. Is E marginally independent of FNoc. Whic
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Homework VII-KEY

1. A graph with no links is a trivial D-Map. True/False

**True. A graph is said to be D- Map of a distribution if all CI satisfied by distribution is reflected on**

the graph, of course graph with no links will reflect any conditional independency.

2. Consider the Bayesian network given below

a. Is A conditionally independent of D give {B,C}.

**Yes,**

b. Is E marginally independent of F

**No**

c. Which edge would you delete to make A independent of C.

**The edge A->C**

3. Evaluate the distribution p(a), p(b|c) and p(c|a) corresponding to the joint distribution given in

the Table. Hence show by direct evaluation that p(a,b,c) = p(a) p(c|a) p(b|c). Draw the

corresponding directed graph.

a | b | c | p(a, b, c)

0 | 0 | 0 | 0.192

0 | 0 | 1 | 0.144

0 | 1 | 0 | 0.048

0 | 1 | 1 | 0.216

1 | 0 | 0 | 0.192

1 | 0 | 1 | 0.064

1 | 1 | 0 | 0.048

1 | 1 | 1 | 0.096**Tables for p(a), p(c|a), p(b|c) evaluated by marginalizing and conditioning the joint distribution from**

the given table.

a | **p(a)**

**0 ** | **0.6**

**1 ** | **0.4**

**a ** | **c ** | **p(c|a)**

**0 ** | **0 ** | **0.4**

**0 ** | **1 ** | **0.6**

**1 ** | **0 ** | **0.6**

**1 ** | **1 ** | **0.4**

**c ** | **b ** | **p(b|c)**

**0 ** | **0 ** | **0.8**

**0 ** | **1 ** | **0.2**

**1 ** | **0 ** | **0.4**

**1 ** | **1 ** | **0.6Multiplying the three distribution together we recover the joint distribution p(a, b, c)given in the**

table, thereby allowing us to verify the validity of the decomposition p(a, b, c) = p(a) * p(c|a) * p(b|c).

We can express the distibution using the graph.

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