A voltage V(t) is a Gaussian, ergodic random process with mean 0 and variance 4 V^2. If measured with a direct-current (DC) meter (i.e., time average reading), what value will the meter indicate?

Introduction / Context:
Understanding what various meters measure for random processes is fundamental in measurement and instrumentation. A DC (average-responding) meter indicates the time-average (mean) value of the input signal. For zero-mean random processes, this has a straightforward implication.

Given Data / Assumptions:

• V(t) is Gaussian and ergodic.
• Mean μ = 0 V.
• Variance σ^2 = 4 V^2 (so rms = √σ^2 = 2 V, but rms is not what a DC meter reads).
• DC meter displays time average (mean) for an ergodic process.

Concept / Approach:
For an ergodic process, the time average equals the ensemble average. A DC meter, which essentially performs a long-time average, therefore indicates the process mean. Since μ = 0, the meter reading is 0 V. Note this differs from an rms-responding meter, which would show 2 V for the given variance.

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