Dgdrxrt

I think I understand the gits of Expectation-Maximization algorithm and its altering nature, but I am puzzled by the notation. Lets see the following examples:

1. in Stanford notes , the E-step is simply stated as posterior probability of latent variable $z$:

$$Q_i(z^(i)) := p(z^(i)|z^(i);theta)$$

where $z^(i)$ is latent variable sample, $x^(i)$ is observed data, $theta$ are the parameters maximized in M-step.

2. in Original paper from 1977 the E-step looks as follows:

$$t^(p) = Ebig[ t(x)|y,Theta^(p) big]$$

where I believe the $y$ is observe variable, $x$ is latent variable, $Theta^(p)$ are model parameters used in M-step. To me, this looks like:

$$E_xbig[ p(x|y,Theta)big]$$

where the $x,y,Theta$ is the same as in point 2.

I appologize for introducing 2 notations, one in point 1. another in point 2. but I am trying to keep it consistent with the linked papers.

Question

The point of E-step is to obtain such values of latent variables, that they maximize the observation of complete data, given the current model parameters $theta$ or $Theta^(p)$. Then my question is, how do I formally get these values from the presented E-steps ?

I mean, what/where do I calculate in $Q_i(z^(i)) := p(z^(i)|z^(i);theta)$ ? Because it is just a definition of posterior distribution, there is no maximization, no operation to be done.

The second one $E_xbig[ p(x|y,Theta)big]$ is a bit more intuitive, because I am calculating an expectation of distributions (I think $t(x)$ is distribution of latent variable $x$). That means, I am looking for such values of $x$, that are expected -> gives maximum probability of realizing/happening.

Can someone formally show (and explain in layman's terms), how to obtain the values of the latent variables from the equations of E-step ?