Practical implementation of Expected Value?
The answer is yes. Even if we could generate several realizations of the random process by conducting the random experiment a number of times. We could only have a limited number of realizations and for a limited period of time practically. Now to take expectation of the random process we will have to take freeze time and look at the distribution of the values across the several realizations we generated. But that would be an estimated expectation because we can only estimate the distribution, because although we have conducted the experiment several times, we cannot practically be sure to exhaust the sample space.