Why is my Gaussian mixture plot reduced proportional in size compared to their univariate normal pdf

Question

I have created a multiples Gaussian distributions using this codes in MATLAB:

mu = [0];
sigma = cat(3, 1);
gmm = gmdistribution(mu, sigma);

figure;
ezplot(@(x) pdf(gmm,x));hold on;

mu = [5]
sigma = cat(3, 2)
gmm = gmdistribution(mu, sigma);

ezplot(@(x) pdf(gmm,x));

When I want to combine both Gaussians with a Gaussian Mixture Model (GMM) using MATLAB, the result is not as I expected. This is the command and the resulting plot:

mu = [0; 5];
sigma = cat(3, 1, 2);
p = [0.5; 0.5];
gmm = gmdistribution(mu, sigma,p);

ezplot(@(x) pdf(gmm,x));

I expect the mixture Gaussian to match the size of the individual Gaussian but it doesn't. I have increased the mixing coefficients for the Gaussian mixture but the result doesn't change. The Gaussian mixture height seems to have been reduced half of the individual Gaussian from the same mean and std deviation.

Answer 1

Because area under density plot should integrate to 1. If mixture would match exactly, area would be >1.