# Definition:Weighted Sum

## Definition

Let $S = \sequence {x_1, x_2, \ldots, x_n}$ be a sequence of real numbers.

Let $\map W x$ be a weight function to be applied to the terms of $S$.

The weighted sum of $S$ is defined as:

$\bar x := \ds \sum_{i \mathop = 1}^n \map W {x_i} x_i$

This means that elements of $S$ with a larger weight contribute more to the weighted sum than those with a smaller weight.

## Sources

$1$: Introduction:
$1.2$ Stochastic and Deterministic Dynamic Mathematical Models
$1.2.1$ Stationary and Nonstationary Stochastic Models for Forecasting and Control: Linear filter model