Consider a decision problem having environmental states X = {x1,x2, X3} with P(X = #1) = 0.21, P(X=x2)= 0.43 and P(X = x3) = 0.36. ppose survey information is available for this decision problem in the form of a survey variable = {81, 82, 83} for which historical data suggests that

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2 Consider a decision problem having environmental states X = {r1, #2, X3} with
P(X = a1) = 0.21, P(X=x2) = 0.43 and P(X = x3) = 0.36.
Suppose survey information is available for this decision problem in the form of a survey variable
S = {s1, 82, $3} for which historical data suggests that
Environment X
P(S|X)
S1
0.40
0.34
0.27
Survey S 82
0.26
0.35 0.32
83
0.34
0.31
0.41
Given this survey information, determine all of the probabilities required to incorporate this
survey information into a decision tree.
Give your answers rounded to 4 decimal places.
Transcribed Image Text:2 Consider a decision problem having environmental states X = {r1, #2, X3} with P(X = a1) = 0.21, P(X=x2) = 0.43 and P(X = x3) = 0.36. Suppose survey information is available for this decision problem in the form of a survey variable S = {s1, 82, $3} for which historical data suggests that Environment X P(S|X) S1 0.40 0.34 0.27 Survey S 82 0.26 0.35 0.32 83 0.34 0.31 0.41 Given this survey information, determine all of the probabilities required to incorporate this survey information into a decision tree. Give your answers rounded to 4 decimal places.
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