Random Signals

The signal v(t) from a voltage source is a binary waveform: it is either 0.5 V or -0.5 V.
The sign change has a 50-50 chance of occurrence within the interval of 1 μs. In other words, v(t) has an equal chance for positive or negative values within this interval.
What is the average and effective values of v(t) over a period of 5 secs?

The string:
S7P3A32 (Force - Push) .
The math:
Pj Problem of interest is of type force. Voltage problems are force problems.
The binary waveform is an example of a non-noise random signal. Random signals are probabilistics. That is, they are specified only partly through their time averages (their mean, rms value, and frequency range). Some examples of random signals are signals picked up by a radio or TV station antenna; the voltage recorded at the terminals of a microphone due to speech utterance; binary waveforms in digital computers; image intensities over the area of a picture; and the speech or music which modulates the amplitude of carrier waves in an AM system.
There are 5(106) intervals during the 5 secs period.
So, average value of v(t), vavg = [0.5(1/2)5(106) - 0.5(1/2)5(106)]/5(106) = 0
Effective value, (veff)2 = [0.52(1/2)5(106) + (-0.5)2(1/2)5(106)]/5(106) = (0.5)2
So, veff = 0.5

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