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P (F - Up) 0.5 P (F - Stable) 0.3 P (F - Down) 0.2 P (U - Up) 0.2 P (U - Stable) 0.3 P (U - Down) 0.5

A manufacturing company is considering two product alternatives, A and B. The expected profits for each product under different demand states (up, stable, down) are provided in a table. The probabilities of each demand state occurring are also given. A test market study will report either a favorable or unfavorable outcome. Conditional probabilities of the market outcome for each demand state are provided. Bayes' theorem should be used to calculate the conditional probabilities of each demand state being true given a favorable or unfavorable market research outcome.

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65 views1 page

P (F - Up) 0.5 P (F - Stable) 0.3 P (F - Down) 0.2 P (U - Up) 0.2 P (U - Stable) 0.3 P (U - Down) 0.5

A manufacturing company is considering two product alternatives, A and B. The expected profits for each product under different demand states (up, stable, down) are provided in a table. The probabilities of each demand state occurring are also given. A test market study will report either a favorable or unfavorable outcome. Conditional probabilities of the market outcome for each demand state are provided. Bayes' theorem should be used to calculate the conditional probabilities of each demand state being true given a favorable or unfavorable market research outcome.

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Al Borja
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© © All Rights Reserved
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57.

 A Manufacturing company introduces two product alternatives. The table below provides profit
payoffs in thousands of dollars.
?
?Bet onState of Nature (Demand)
?UpStableDown
?Product A1188
?Product B81012
?
?
?
The probabilities for the state of nature are P(Up) = 0.35, P(Stable) = 0.35, and P(Down) = 0.30.
A test market study of the potential demand for the product is expected to report either a favorable (F) or
unfavorable (U) condition. The relevant conditional probabilities are as follows:
P(F|Up) = 0.5; P(F|Stable) = 0.3; P(F|Down) = 0.2
P(U|Up) = 0.2; P(U|Stable) = 0.3; P(U|Down) = 0.5
Use Bayes’ theorem to compute the conditional probability of the demand being up, stable, or down,
given each market research outcome.
ANSWER:  
Let s1 = Demand is up
s2 = Demand is stable
s3 = Demand is down

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