when is false: is the same as and are not independent

when is true: we do not care about because is always true and are independent

when is false: which means that and are both false when we know one of them is false, then we already know the other is false and are independent.

when is true: we do not know which of and made is true.

2. Tree-Structured CPDs

Example:

if , then the recruiter do not looks at letter, so is independent of .

if , the and are independent of like what shown in the tree structure.

if the and are independent of

if and for both value of , so the statement here has two cases: and so in both the cases, the statement is true.

An example of multiplexer: the choice variable determines the circumstance or another set of circumstance.

Question:

Analysis:

given observed , active the active trail of

if we know , which means that the arrow between and is disappear, while if we know the arrow between and is disappear(like what we shown below).

A tell us which of the variable , need to copy.

Summary

3. Independence of Causal Influence

Sometimes it's not the case that you depend on one only in certain contexts, and not in others. Really, you depend on all of them and all of them sort of contribute something to the probability of

Sigmoid CPD

An intuitive view:

Choices:

4. Continuous Variables

The (inside temperature) is the linear combination of (current temperature) and (outside temperature).