deletions | additions       diff --git a/GMM.tex b/GMM.tex  index 7c949c5..0d31b72 100644  --- a/GMM.tex  +++ b/GMM.tex 
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$T^{(t)}_{j,i}=P(Z_i=j|X_i=x_i,\theta^{(t)})=\frac{P(z_{j})f(x_i|\mu^{(t)}_{j}, \sigma^{2(t)}_{j})}{p^{(t)} f(x_i|\mu^{(t)}_{1}, \sigma^{2(t)}_{1})+(1-p^{(t)})f(x_i|\mu^{(t)}_{2}, \sigma^{2(t)}_{2})}$  $Q(\mathbf{\theta}|\mathbf{\theta^{(t)}})=E_{\textbf{z}|\textbf{x},\mathbf{\theta^{(t)}}}(\log L(\mathbf{\theta};\textbf{x};\textbf{z})) =E[( \log \prod \limits_{i=1}^n L(\mathbf{\theta};x_{i};z_{i})] =  \sum\limits_{i=1}^n E[( \log L(\mathbf{\theta};x_{i};z_{i})] = =$  $=  \sum\limits_{i=1}^n \sum\limits_{j=1}^2 T^{(t)}_{j,i}[\log P(z_{j}) -\frac{1}{2}\log(2\pi) - \frac{1}{2}\log\sigma^{2}_{j} - \frac{(x_{i}-\mu_{j})^2}{2\sigma^{2}_{j}}]$ \textit{M-step}