Solutions 1

Exercise 1.1:

  1. 2/3, 1/3 and 1/2
  2. The certainty will be close to zero. Note that the certainty from the combined actions is much smaller than the minimum of the effects of single actions.

Exercise 1.2:

The structure should be similar to the structure of the "Car Start" model.

Exercise 1.3:

  1. All variables are d-connected to A given evidence on B.
  2. All variables (except C and F) are d-connected to A given evidence on J.

Exercise 1.5:

The DAGs (a), (b) and (c) are I-equivalent.

Exercise 1.6:

P(A) = (0.2,0.4,0.4)
P(B) = (0.3,0.3,0.4)
P(A|B)=
b1b2b3
a10.1670.3330.125
a20.500.625
a30.3330.6670.25
P(B|A)=
b1b2b3
a10.250.50.25
a20.37500.625
a30.250.50.25