Question

Average power in a random process is​

Answer 1

The first definition works for deterministic as well as for random signals. For random signals we define the autocorrelation by

Rx(τ)=E{x∗(t)x(t+τ)}(1)

where E{⋅} is the expectation operator. For deterministic power signals (i.e., signals with finite but non-zero power and infinite energy) we define

Rx(τ)=limT→∞12T∫T−Tx∗(t)x(t+τ)dt(2)

From (2) it is clear that for deterministic power signals both definitions of average power are equivalent, because for random signals as well as for deterministic power signals we have

Sx(f)=F{Rx(τ)}(3)

Also take a look at this related answer.

You are right about the power of white noise. In continuous time, white noise has infinite power. Only discrete-time white noise has finite power. In sum, teachers and professors are only humans.

Answer 2

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If the random variable represents a random voltage or current, then the first moment m1 = η represents the DC component, the second moment m2 represents the total average power, the second central moment (the variance σ2 rep- resents the average power in the AC component and the mean squared η2 represents the power in .