how find optimal threshold?

Hi I have this code and my density functions are P(w1)=1/3 and P(w2)=2/3

x = [-5:.1:5];
plota = normpdf(x,0,1);
plotb = normpdf(x,1,0.8);
figure; hold on;
plot(x,plota,'r');
plot(x,plotb,'b');

How can I get optimal threshold like this

Answer 1

[Star Strider]

I am not certain what you are asking.

The ‘threshold’ as illustrated would be the mean (or median) of the selected normal distribution.

To get ‘area1’ and ‘area2’ —

x = [-5:.01:5];
plota = normpdf(x,0,1);
plotb = normpdf(x,1,0.8);

mean_a = mean(plota);
x_b = normpdf(mean_a,1,0.8);
area_a = 1 - normcdf(mean_a,0,1)

area_a = 0.4602

area_b = 1 - normcdf(mean_a,1,0.8)

area_b = 0.8697

figure
hold on
plot(x,plota,'r')
plot(x,plotb,'b')
plot([1 1]*mean_a, [0 1]*normpdf(mean_a,0,1), '--k')
patch([x(x>=mean_a) flip(x(x>=mean_a))], [zeros(size(x(x>=mean_a))) flip(normpdf(x(x>=mean_a),0,1))],'r', 'FaceAlpha',0.5)
patch([x(x>=mean_a) flip(x(x>=mean_a))], [zeros(size(x(x>=mean_a))) flip(normpdf(x(x>=mean_a),1,0.8))],'b', 'FaceAlpha',0.5)
hold off

I am not certain where you want to go from there.

.