Essays on The Key Aspects of Evaluating Risk Management in Agribusiness Assignment

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The paper "The Key Aspects of Evaluating Risk Management in Agribusiness" is a great example of a Business assignment.   Question One: Estimation of Joint, marginal and posterior probabilities, and Bayes’ theorem Joint probability; The joint probability measures the likelihood of two events occurring at the same time. The calculation below shows risk exposure by the farmers as a result of potato late blight fungus (PLBF); Unlikely scenario   P (Z1S1) = 0.4 X 0.7= 0.28 P (Z1S2) = 0.4 X 0.6= 0.24 P (Z1S3) = 0.4 X 0.2= 0.08 Possible Scenario P (Z2S1) = 0.4 X 0.2= 0.08 P (Z2S2) = 0.4 X 0.2= 0.08 P (Z2S3) = 0.4 X 0.3= 0.12 Probable Scenario P (Z3S1) = 0.2 X 0.1= 0.02 P (Z3S2) = 0.2 X 0.2= 0.04 P (Z3S3) = 0.2 X 0.5= 0.10 Marginal probability; The marginal probability shows the likelihood of PLBF from subsets of randomly collected variables of unlikely, possible and probable occurrence.

The Marginal probability of PLBF is given by (PZ1) =P (S1 and Z1) + P (S2 and Z1) + P (S3 and Z1) P (Z1) = (0.4 X 0.7) + (0.4 X 0.6) + (0.2 X 0.2) = 0.56 P (Z2) = (0.4X0.2) + (0.4X0.2) + (0.2X0.3) = 0.22 P (Z3) = (0.4X0.1) + (0.4X0.2) + (0.2X0.5) = 0.22 Posterior probability; The probability shows probability of event (A) occurring because another event (B) has occurred.

The calculation below shows posterior probability; P (SiǀZk) = P (Zk and Si) / P(Zk) P (S1/Z1) = =0.500                        P (S2/Z1) =   = 0.429                              P (S3/Z1) =   = 0.143 P (S1/Z2) = =0.364                        P (S2/Z2) =   = 0.364                              P (S3/Z2) =   = 0.545 P (S1/Z3) = =0.091                    P (S2/Z3) =   = 0.182                                  P (S3/Z3) =   = 0.455 Bayes’ Theorem;   A B C D E F G H I 1 State Prior Likelihoods P(Zk/Si)   Joint Probabilities P(Si and Zk) 2 Sn P(Sn) Z1 Z2 Z3   Z1 Z2 Z3 3 S1 0.4 0.7 0.2 0.1   0.28 0.08 0.04 4 S2 0.4 0.6 0.2 0.2   0.24 0.08 0.08 5 S3 0.2 0.2 0.3 0.5   0.04 0.06 0.1 6 Check 1.0 Marginal P(Zk) 0.56 0.22 0.22 7     Posterior P(S1/Zk) 0.500 0.429 0.143 8       P(S2/Zk) 0.364 0.364 0.545 9       P(S3/Zk) 0.091 0.182 0.455 10           Check 1.0 1.0 1.0  

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