Probability and Learning

A$.$ Let us consider the "Nixon diamond" from a probabilitistic viewpoint. We

will also make it more specific by turning "being a pacifist" into "supported

American involvement in the Vietnam war in $1968"($the year Richard Nixon

was elected president of the United States$).$ Assume $($and some of these are

guesses$)$:

In $1968,0\mathrm{.}06139\%$ of the American population is Quaker

In $1968,27\%$ of the American population is Republican

In $1968,40\%$ of the Americans who are not Republican supported

American involvement in the Vietnam War

In $1968,80\%$ of the American Quakers did not support American

involvement in the Vietnam war$)$

In $1968,55\%$ of the American Republicans supported American

involvement in the Vietnam war

In $1968,$ most American Quakers were not Republican

However, in $1968$ among Americans who were Quaker and Republican,

most supported American involvement in the Vietnam war. Richard

Nixon was an example because he expanded the Vietnam War into Laos

and Cambodia.

Construct a Bayesian Network that describes the relation among the

variables

Give this Bayesian Network conditional or prior probability values at

each node from the data above and reasonable assumptions. Please

state your assumption.

B$.$ Consider the following data:

Show that attribute Attribute is useless $($provides no information$)$ to learn

LearnMe.