- #1

Frank Einstein

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- TL;DR Summary
- I am trying to understand an example which doesn't seem to make sense

Hello everyone. I am currently reading the book

<X(t)>

Which shows that a stationary process isn't necessary ergodic. However, in the very next page the book states that <X(t)>

Any answer is appreciated.

Regards.

*Probability statistics and random processes for electrical engineering*by Alberto Leon Garcia. In page 540, one can find example 9.47, in which is shown how a stationary random process doesn't have to be ergodic by defining a random variable A of zero mean and variance one. Then, a stochastic process is defined as X(t)=A, therefore,*m*_{X}(t)= E[X(t)]=E[A]=0. However, the integration over a time interval returns<X(t)>

_{T}=∫_{-T}^{T}A dt=AWhich shows that a stationary process isn't necessary ergodic. However, in the very next page the book states that <X(t)>

_{T}is an unbiased estimator of*m.*Am I understanding everything wrong or these two statements contradict each other?Any answer is appreciated.

Regards.