Solve the following questions using any source of information from books, Internet, etc. It is recommended to use MATLAB for plotting the graphs and writing the necessary codes. Include all your graphs, codes and references for the solution of the following questions.

Let p(s|genuine) ~ N(80, 20) and p(s|impostor) ~ N(60, 20) for a certain biometric system, where N( µ,σ ) represents a Gaussian distribution with mean µ and standard deviation σ . Suppose thefollowing decision rule is employed: Assign s to the genuine class if s > η , else assign s to theimpostor class. Here, η ∈ (- ∞ ,∞ ).

(a) Plot these two distributions. If η = 80, what is the FAR and FRR of the biometric system?

(b) Report the EER and d-prime value based on these distributions (do not use the ROC curve to compute the EER).

(c) Plot the ROC curve.