2 Consider a decision problem having environmental states X = {x₁, x2, x3} with P(X = x₁) = 0.56 and P(X= x3) = 0.17. Suppose survey information is available for this decision problem in the form of a survey variable S = {81, 82, 83} for which historical data suggests that P(S|X) Survey S $1 S2 $3 Environment X x3 X1 0.13 0.48 x2 0.18 0.31 0.74 0.22 Given this survey information, determine all of the probabilities required to incorporate this survey information into a decision tree.

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2 Consider a decision problem having environmental states X = {x₁, x2, x3} with
P(X = x₁) = 0.56 and P(X = x3) = 0.17.
Suppose survey information is available for this decision problem in the form of a survey variable
S = {81, 82, 83} for which historical data suggests that
P(S|X)
Survey S
Environment X
x3
X1 x2
0.13 0.18
$1
S2 0.48
$3
0.31
0.74 0.22
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 = {x₁, x2, x3} with P(X = x₁) = 0.56 and P(X = x3) = 0.17. Suppose survey information is available for this decision problem in the form of a survey variable S = {81, 82, 83} for which historical data suggests that P(S|X) Survey S Environment X x3 X1 x2 0.13 0.18 $1 S2 0.48 $3 0.31 0.74 0.22 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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