he table contains raw match scores for 10 subjects with 3 samples for each subject.  You may assume the system is symmetric. You may use the tool of your choice(R, Python, Excel, Matlab, etc) in the analysis of the data. But please indicate which tool is being used. What does it mean when we refer to a biometric as symmetric? What is the meaning of Determine the total number of scores that have been generated? How many imposter scores can be generated? How many genuine? Plot the genuine and imposter match score distributions. Generate a set of 10 thresholds, determine the FAR and FRR at each threshold value. Plot the ROC Curve for your data (FAR vs. FRR and GAR vs. FRR). Plot error rates relative to the threshold score and indicate the point where the EER occurs. What is the EER of the system? What threshold value would you select for a high-security application?  What are the implications of your selection? Provide a justification for your response. What threshold value would you select for a forensic application?  What are the implications of your selection? Provide a justification for your response. What is the AUC of the system? What is the d-prime value for this system?

A biometric is referred to as symmetric when the comparison scores obtained from matching one sample to another are the same regardless of the order in which the samples are presented. In other words, if we compare sample A to sample B and then compare sample B to sample A, the resulting scores should be equal.

To determine the total number of scores that have been generated, we can multiply the number of subjects by the number of samples per subject. In this case, since there are 10 subjects and 3 samples per subject, the total number of scores would be 10 * 3 = 30.

Imposter scores represent the comparison scores between samples from different subjects, while genuine scores represent the comparison scores between samples from the same subject. Since there are 10 subjects, there can be a maximum of 10 * (10-1) = 90 imposter scores, as each subject can be compared with 9 other subjects. The number of genuine scores would be equal to the total number of scores (30), as each subject can be compared with itself.

To plot the genuine and imposter match score distributions, we need to create a histogram or a density plot of the scores. The x-axis would represent the score values, and the y-axis would represent the frequency or density of occurrence for each score. This can be done using any tool like R, Python, Excel, Matlab, etc.

To generate a set of 10 thresholds, we can divide the range of match scores into 10 equally spaced intervals. We can then calculate the False Acceptance Rate (FAR) and False Rejection Rate (FRR) at each threshold value. The FAR represents the probability of incorrectly accepting an imposter, while the FRR represents the probability of incorrectly rejecting a genuine subject.

The Receiver Operating Characteristic (ROC) curve can be plotted by plotting the FAR against the FRR. Additionally, we can plot the Genuine Accept Rate (GAR) against the FRR. The GAR represents the probability of correctly accepting a genuine subject. This can be done using tools like R, Python, Excel, Matlab, etc.

The Equal Error Rate (EER) is the point on the ROC curve where the FAR is equal to the FRR. In other words, it represents the threshold value at which the error rates for imposter and genuine classifications are equal. We can determine the EER of the system by finding this point on the ROC curve.

For a high-security application, we would select a threshold value that minimizes the FAR while keeping the FRR within an acceptable range. This would ensure a low probability of incorrectly accepting imposters while maintaining a reasonable probability of correctly accepting genuine subjects. The implications of this selection would be a higher level of security but potentially a higher rate of false rejections.

For a forensic application, we would select a threshold value that minimizes the FRR while keeping the FAR within an acceptable range. This would ensure a low probability of incorrectly rejecting genuine subjects while maintaining a reasonable probability of correctly rejecting imposters. The implications of this selection would be a higher level of confidence in identifying genuine subjects, but potentially a higher rate of false acceptances.

The Area under the ROC Curve (AUC) is a measure of the overall performance of a biometric system. It represents the probability that a randomly chosen genuine subject has a higher match score than a randomly chosen imposter. The AUC values range from 0.5 (random guessing) to 1 (perfect classification).

The d-prime value for the system represents the separability between genuine and imposter distributions. It is a measure of the discriminability of the biometric system and can be calculated using statistical methods such as Signal Detection Theory. A higher d-prime value indicates better separability and performance of the system.

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