Expected value of signals
This is the cross-correlation function of the two discrete-time random processes $x[n]$ and $y[n]$. It measures the similarity of the processes for a given time lag between the two. If $x[n]$ and $y[n]$ are jointly wide-sense stationary, then the cross-correlation only depends on the lag $k$, and not on the absolute time index $n$.

In terms of probabilities (or rather probability density functions), the expectation $E\{x[n]y[n-k]\}$ is given by

$$E\{x[n]y[n-k]\}=\int_{-\infty}^{\infty}xyf_{XY}(x,y;n,n-k)dxdy$$

where $f_{XY}(x,y;n_1,n_2)$ is the joint probability density function of $x[n_1]$ and $y[n_2]$.

In practice, we usually hope that the processes are ergodic, which allows us to estimate such an expectation by taking the appropriate time averages.