Discuss the bayes net on 5 binary variables, Basic Statistics

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Discuss the bayes net on 5 binary variables

Assignment:

PART 1

a. Use the chain rule to rewrite P(A,B,C,D,E) for the variables in the graphical model below.

b. Investigate every triple in this graph. Use the d-separation algorithm to explain why each tripledoes or does not give rise to a conditional independence

1224_D 3.jpg

PART 2

Consider the following Bayes' net on 5 binary variables: Smart, Study, Prepared, Fair, Pass.

a. What is the probability that a student who passed is smart?

b. What is the probability that a student who passed an unfair exam is smart?

c. How many roots are there here?

d. What is the probability that a student studied, given that she passed the exam?

81_D 4.jpg

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