# Dictionary:Expectation

1. An operator that denotes the mean, or weighted mean where values are not equally probable. Usually denoted by braces, ${\displaystyle E\{\ldots \}}$.
2. In seismic processing usage, it indicates the sum of elements for finite wavelets ${\displaystyle \left(b_{t}\right)}$, or the mean of an infinite time series ${\displaystyle \left(u_{t}\right)}$:
${\displaystyle E\{b_{t}\}=b_{1}+b_{2}+b_{3}+\ldots +b_{n}}$, or
${\displaystyle E\{b_{t}\}=\lim _{n\to \infty }{\frac {u_{-n}+u_{-n+1}+\ldots +u_{0}+u_{1}+u_{2}+\ldots +u_{n}}{2n+1}}}$