Properties of Stochastic Processes I have a basic question about stochastic processes:

When some informations such as wss, uncorraleted sampled, white about random signal (say x[n]) are given, what do we exactly have?


For example white information:
I know if x[n] is white, its power density function $ P_{x}(e^{j\omega}) $ is constant value independent of $ \omega $. I suppose it means autocorrelation function of x[n] consists of dirac? (I am not sure here, If I am wrong, please correct me). 
Uncorraleted samples: I know if the random signal is uncorrelated, its covariance equals to zero which means its autocorrelation equals to square of its mean. But uncorraleted samples means this, or something else?
What about wss?: I know if the signal is wss, mean (average) of x[n] is constant which is useful information when $ x_{c}(t) $ (constinuous time form of x[n]) and its means are given and we can say directly mean of x[n] is the same as mean of $ x_{c}(t) $. Moreover, we have $ \phi_{x}[m]  =  \phi_{x_{c}}[mT] $ where T is the sampling period and $ \mu_{x_{c}}^{2} = \mu_{x}^{2} $ where $ \mu $ is the power of the signals (second moment).


Any correction, addition, comment would be appreciated.



Pass through an example may be more convenient:

Suppose we have a system like this:



where, x[n]: wss, $ \eta_{x} = 0 $ (mean value), uncorrelated samples, $ \sigma_{x}^{2} $ and h[n] are given.


How to calculate $ \eta_{y}[m] $ the mean, $ \phi_{y}[m] $ the autocorrelation and $ \mu_{y}[m] $ the average power of y[n]?
How to calculate $ \eta_{v}[m] $ the mean, $ \phi_{v}[m] $ the autocorrelation and $ \mu_{v}[m] $ the average power of v[n]?
As pointed out in the comments, this question is rather broad, so here I will just answer your last question about the autocorrelation of the output signal $y[n]$. You might know the following relation concerning the power spectra of input and output sequences:

$$S_y(\omega)=S_x(\omega)|H(\omega)|^2\tag{1}$$

where $H(\omega)$ is the frequency response of the LTI system. From the inverse Fourier transform of (1) you get a corresponding relation between the autocorrelation functions:

$$\phi_y[m]=\phi_x[m]\star h[m]\star h^*[-m]\tag{2}$$

where $h[m]$ is the system's impulse response, and $\star$ denotes convolution.