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Sample Mean


Definition: The sample mean of a set of $ N$ samples from a particular realization of a stationary stochastic process $ v$ is defined as the average of those samples:

$\displaystyle \hat{\mu}_{v} \isdef {\cal E}_N\{v(0:N-1)\} \isdef \frac{1}{N}\sum_{n=0}^{N-1} v(n)$ (C.17)

For a stationary stochastic process $ v$ , the sample mean is an unbiased estimator of the mean, i.e.,

$\displaystyle E\{\hat{\mu}_{v}\} = \mu_v.$ (C.18)

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