Gaussian Mixture Models

Question

I am trying to understand the Gaussian Mixture Model but I am stuck trying to understand the concept.

Given a joint probability $p(x,z)$

$$p(x) = \pi_0f_0(x) + \pi_1f_1(x)+...+\pi_nf_n(x)$$

I understand the $f_o,f_1,...,f_n$ are PDF of Gaussian distributions, but what are the $\pi_o,\pi_1,...,\pi_n$

Answer 1

$\pi_i$'s are the probabilities (i.e. weights) that an observation is sampled from $f_i(x)$, $i = 0,1,\ldots,n$.