%4a
C=norminv(0.05,0); %calculating c where false alarm rate is 0.05 and mu=0
D=norminv(0.9)-C; %since d'=distance between noise's center and noise+center now we
know the mu of noise+signal but without zero sign
Beta=exp(D*(C-(D/2)));
C_interval=-10:0.1:10;
False_alarm_rate=zeros(1,size(C_interval,2)); %creating empty matrices
Hit_rate=zeros(1,size(C_interval,2));
beta=zeros(1,size(C_interval,2));
for ii=1:length(C_interval)
False_alarm_rate(1,ii)=1-normcdf(C_interval(ii),0,1); %probability of false
Hit_rate(1,ii)=1-normcdf(C_interval(ii),D,1);
beta(1,ii)=normpdf(C_interval(ii),D,1)/normpdf(C_interval(ii),0,1);
end
figure
plot(False_alarm_rate,Hit_rate); xlabel('False Alarm Rate') ;ylabel('Hit Rate') ;title('ROC')
xlim([0 1]); ylim([0 1])
C=norminv(0.05,0); %calculating c where false alarm rate is 0.05 and mu=0
D=norminv(0.9)-C; %since d'=distance between noise's center and noise+center now we
know the mu of noise+signal but without zero sign
Beta=exp(D*(C-(D/2)));
C_interval=-10:0.1:10;
False_alarm_rate=zeros(1,size(C_interval,2)); %creating empty matrices
Hit_rate=zeros(1,size(C_interval,2));
beta=zeros(1,size(C_interval,2));
for ii=1:length(C_interval)
False_alarm_rate(1,ii)=1-normcdf(C_interval(ii),0,1); %probability of false
Hit_rate(1,ii)=1-normcdf(C_interval(ii),D,1);
beta(1,ii)=normpdf(C_interval(ii),D,1)/normpdf(C_interval(ii),0,1);
end
figure
plot(False_alarm_rate,Hit_rate); xlabel('False Alarm Rate') ;ylabel('Hit Rate') ;title('ROC')
xlim([0 1]); ylim([0 1])
