2 Consider a decision problem having environmental states X {x1, x2, x3} with P(X = x1) = 0.21, P(X = x2) = 0.43 and P(X = x3) = 0.36. %3D %3D ippose survey information is available for this decision problem in the form of a survey variable {$1, $2, $3} for which historical data suggests that Environment X

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2 Consider a decision problem having environmental states X = {x1, x2, x3} with
P(X = x1) = 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
S = {$1, 82, 83} for which historical data suggests that
a
survey
variable
Environment X
P(S|X)
X1
X2
X3
S1
0.40
0.34
0.27
Survey S
S2
0.26
0.35
0.32
S3
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 = {x1, x2, x3} with P(X = x1) = 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 S = {$1, 82, 83} for which historical data suggests that a survey variable Environment X P(S|X) X1 X2 X3 S1 0.40 0.34 0.27 Survey S S2 0.26 0.35 0.32 S3 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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