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import numpy as np
import matplotlib.pyplot as plt
def expected_value(prob_storm, sensitivity, specificity, prob_mold, prob_high_sugar, prob_low_sugar, prob_regular_sugar):
payout_matrix = np.matrix([6000*5+2000*10+2000*15,
5000*5+1000*10+2000*120,
5000*5+1000*10,
4000*5+2500*10+2000*15+1000*30+500*40,
6000*5+2000*10+2000*15,
5000*5+1000*10+2500*15+1500*30])
payout_matrix = payout_matrix * 12
def s_branch(payout_matrix,prob_mold):
return(prob_mold * payout_matrix[0,1] + (1-prob_mold) * payout_matrix[0,2])
def ns_branch(payout_matrix,prob_high_sugar,prob_low_sugar,prob_regular_sugar):
return(prob_high_sugar * payout_matrix[0,3] + prob_low_sugar*payout_matrix[0,4] + prob_regular_sugar*payout_matrix[0,5])
P_DS = sensitivity * (prob_storm) + (1-sensitivity) * (1-prob_storm)
P_DNS = specificity * (1-prob_storm) + (1-specificity) * prob_storm
P_S_DS = (sensitivity * prob_storm)/P_DS
P_NS_DS = 1 - P_S_DS
E_val_top = []
E_val_top.append(payout_matrix[0,0])
E_val_top.append(s_branch(payout_matrix,prob_mold) * P_S_DS + P_NS_DS * ns_branch(payout_matrix,prob_high_sugar,prob_low_sugar,prob_regular_sugar))
P_NS_DNS = (specificity * (1-prob_storm))/P_DNS
P_S_DNS = 1-P_NS_DNS
E_val_bot = []
E_val_bot.append(payout_matrix[0,0])
E_val_bot.append(s_branch(payout_matrix,prob_mold) * P_S_DNS + P_NS_DNS*ns_branch(payout_matrix,prob_high_sugar,prob_low_sugar,prob_regular_sugar))
result = np.max(E_val_top) * P_DS + np.max(E_val_bot)* (1-P_DS)
return (result - payout_matrix[0,0])
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