SI&DA - Definition of 'Confidence Interval'

Definition of ‘Confidence Interval’

SIandDADefinition

Given a RV: $X$ with mean $E[X]=m_x$ and variance ${\sigma }_x$ we define the **$k$ - confidence interval$\ast \ast (:=$\alpha_k$) as:

As we can see for the Gaussian Distribution we can say that the 3-confidence interval is over 99% → This means that we are 99.7% sure that an observation of this Random Process will fall into the 3 interval range centred in the mean of the process ($m_x$)