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Math Help - Business math

  1. #1
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    Business math

    6. A farmer wants to plant one of three crops: wheat, corn, or soybeans. The amount of rain received will determine how well or poor the crop does. The payoffs are:

    Decision State of Nature
    Crop Abundant Rain (a) Marginal Rain (m)
    Wheat $5,000 $3,000
    Corn $10,000 $-4,000
    Soybeans $3,000 $1,000

    Given:
    (1) Prior data: P(a) = .60 and P(m) = .40
    (2) Additional Information:

    The farmer considers hiring a weather forecaster to get additional understanding of the expected weather for the year. The forecaster will report the weather will be either wet or dry.
    a = Abundant rain
    m = Marginal rain
    W = Wet weather forecast
    D = Dry weather forecast

    Conditional Probabilities


    P (W|a) = .80
    P (D|a) = .20
    P (W|m) = .10
    P (D|m) = .90

    Questions:
    (1) Draw a decision tree for the overall situation.

    (2) Calculate the Posterior Probabilities of (D) and P(W).
    (3) How much should he consider paying the weather forecaster? What is the maximum for this payment?
    (4) Determine the efficiency of the additional information?
    (5) What is the farmer’s decision strategy?
    Last edited by lillian; August 2nd 2007 at 07:38 AM. Reason: missing the question
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by lillian View Post
    6. A farmer wants to plant one of three crops: wheat, corn, or soybeans. The amount of rain received will determine how well or poor the crop does. The payoffs are:

    Decision State of Nature
    Crop Abundant Rain (a) Marginal Rain (m)
    Wheat $5,000 $3,000
    Corn $10,000 $-4,000
    Soybeans $3,000 $1,000

    Given:
    (1) Prior data: P(a) = .60 and P(m) = .40
    (2) Additional Information:

    The farmer considers hiring a weather forecaster to get additional understanding of the expected weather for the year. The forecaster will report the weather will be either wet or dry.
    a = Abundant rain
    m = Marginal rain
    W = Wet weather forecast
    D = Dry weather forecast

    Conditional Probabilities


    P (W|a) = .80
    P (D|a) = .20
    P (W|m) = .10
    P (D|m) = .90

    Questions:
    (1) Draw a decision tree for the overall situation.
    Decision tree attached

    RonL
    Attached Thumbnails Attached Thumbnails Business math-gash.jpg  
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by lillian View Post
    6. A farmer wants to plant one of three crops: wheat, corn, or soybeans. The amount of rain received will determine how well or poor the crop does. The payoffs are:

    Decision State of Nature
    Crop Abundant Rain (a) Marginal Rain (m)
    Wheat $5,000 $3,000
    Corn $10,000 $-4,000
    Soybeans $3,000 $1,000

    Given:
    (1) Prior data: P(a) = .60 and P(m) = .40
    (2) Additional Information:

    The farmer considers hiring a weather forecaster to get additional understanding of the expected weather for the year. The forecaster will report the weather will be either wet or dry.
    a = Abundant rain
    m = Marginal rain
    W = Wet weather forecast
    D = Dry weather forecast

    Conditional Probabilities


    P (W|a) = .80
    P (D|a) = .20
    P (W|m) = .10
    P (D|m) = .90

    Questions:
    (1) Draw a decision tree for the overall situation.

    (2) Calculate the Posterior Probabilities of (D) and P(W).
    P(W)= P(W|a)p(a) + P(W|m)p(m) = 0.8\times 0.6 + 0.1 \times 0.4=0.52

    P(D)= P(D|a)p(a) + P(D|m)p(m) = 0.2\times 0.6 + 0.9 \times 0.4=0.48

    RonL
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by lillian View Post
    6. A farmer wants to plant one of three crops: wheat, corn, or soybeans. The amount of rain received will determine how well or poor the crop does. The payoffs are:

    Decision State of Nature
    Crop Abundant Rain (a) Marginal Rain (m)
    Wheat $5,000 $3,000
    Corn $10,000 $-4,000
    Soybeans $3,000 $1,000

    Given:
    (1) Prior data: P(a) = .60 and P(m) = .40
    (2) Additional Information:

    The farmer considers hiring a weather forecaster to get additional understanding of the expected weather for the year. The forecaster will report the weather will be either wet or dry.
    a = Abundant rain
    m = Marginal rain
    W = Wet weather forecast
    D = Dry weather forecast

    Conditional Probabilities


    P (W|a) = .80
    P (D|a) = .20
    P (W|m) = .10
    P (D|m) = .90

    Questions:
    (1) Draw a decision tree for the overall situation.

    (2) Calculate the Posterior Probabilities of (D) and P(W).
    (3) How much should he consider paying the weather forecaster? What is the maximum for this payment?
    The maximum he should pay is the difference between the expected return
    if he plants optimally with the forcast and the expected return if he plants
    optimally without the forcast.

    However I would be tempted to pay less.

    RonL
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  5. #5
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    This is my answer- thanks for help

    :d
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