# Does lim (t to infty) E(x-x hat) = 0 imply that there will be less disturbance over time?

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${\displaystyle E(x)\,}$ here denotes the expected value of ${\displaystyle x\,}$, where ${\displaystyle x\,}$ is a random variable. ${\displaystyle \lim _{t\to \infty }E(x-{\hat {x}})=0\,}$ only implies that the mean estimation error will converge to zero over time. Disturbance, however, will affect the variance of the error, which is given by ${\displaystyle E(x-{\hat {x}})^{2}\,}$. In CDS 110b, we will learn how to design observers that minimize this estimation variance if the disturbance can be modeled as Gaussian noise.