### consider the following decision network influence diagram a v pcw 1 a v 1 d 0 4 10 9 5150506

Consider the following decision network (influence diagram). A V PCW-1 A,V) 1 D 0.4 10.9 2 0 0.2 2 10.7 P(X=1)=0.6 A X P(V=AX) To 0.5 10.9 20/0.3 ” W 2 10.6 sok A WLUCAW) To 1112 20 2110 1. Compute the expected utility of taking action A = 2 given as evidence X = 1. E[U (2. W) A = 2, X = 1) = 2. Suppose that an agent computes the conditional expected utility of taking each action given evidence X = 0 to be the following: E[U (1, W A = 1, X = 0 = 7.45 and EU (2,W) A = 2, X = 0) = 3.50 . Assuming that the agent's computation is correct, which action would the agent choose and why? What is the expected utility EU (al X = 0) (using the notation in the textbook) of the optimal action a given the evidence?