The probability that the majority of a three person jury will convict a guilty person is given by the formula P (x, y, z) = xy(1 − z) + (1 − x)yz + (1 − y)xz + xyz subject to constraint x + y + z = α, where x, y, z represents each jury members’ probability of reaching a guilty verdict and α is some constant that is generally less than or equal to the number of jurors. Find the values of x, y and z that maximizes the probability of convicting a guilty person when α = 0.75
The probability that the majority of a three person jury will convict a guilty person is given by the formula P (x, y, z) = xy(1 − z) + (1 − x)yz + (1 − y)xz + xyz subject to constraint x + y + z = α, where x, y, z represents each jury members’ probability of reaching a guilty verdict and α is some constant that is generally less than or equal to the number of jurors. Find the values of x, y and z that maximizes the probability of convicting a guilty person when α = 0.75
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The probability that the majority of a three person jury will convict a guilty
person is given by the formula
P (x, y, z) = xy(1 − z) + (1 − x)yz + (1 − y)xz + xyz
subject to constraint x + y + z = α, where x, y, z represents each jury members’
probability of reaching a guilty verdict and α is some constant that is generally
less than or equal to the number of jurors. Find the values of x, y and z that
maximizes the probability of convicting a guilty person when α = 0.75
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