The expectations or ensemble average of a random process x(t) are averages "across the process".

The DC value of x(t) is defined by the time average

The other time average of particular interest is the autocorrelation function R_x(t, T) defined in terms of the sample function x(t) observed over the interval - T ≤ t ≤ T.

Following equation, we may formally define the time-averaged autocorrelation function of a sample function x(t) as follows :

This second time-average should also be viewed as a random variable with a mean and variance of its own.

In a manner similar to ergodicity of the mean, we say that the process x(t) is ergodic in the autocorrelation function if the following two limiting conditions are satisfied :

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For signal x(- t) to be causal, the original signal x(t) has to be anticausal.

Similarly for signal x(- t) to be non causal, the original signal x(t) has to be causal.

Hence response of x(t) depends solely on x(t) only.

The T.F.

10³ = 100 - 10³ x 100 x β

900 = - 100000 x β

∴ β = - 9 x 10^-3.

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Apply KCL at node A

V_B = 5 x 1 5 V

∴ V_AB = V_A - V_B = 1.33 - 5 = - 3.67 V