# Is the expectation of a random process $X(t)$ with zero DC component necessarily zero?

Is the expectation of a random process $$X(t)$$ with zero DC component necessarily zero? Or can it be non-zero depending upon the process?

• no, the pdf of amplitudes is symmetric around zero. another way of looking at it is the AC electrical power socket produces power but has a mean voltage of zero – user28715 Jul 10 '19 at 16:58
• What is the DC component of a random process? How is it defined? – Dilip Sarwate Jul 10 '19 at 18:17
• $X(t)$ is said to have a DC component of $A$ if $X(t) = Y(t) + A$ , where $Y(t)$ has zero DC component. – helloworld1e. Jul 11 '19 at 1:00
• That just begs the question since you still haven’t told us what it means for a process to have a zero DC component. – Dilip Sarwate Jul 11 '19 at 1:35
• My guess is the OP is assuming a random process to be DC free iff its power spectral density is zero at $\omega = 0$. But that's just guessing really. So far we don't even know if the process is assumed to be stationary? – Florian Jul 11 '19 at 7:15