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GATE 2019 EE – Question 15

Engineering Mathematics · Probability and Statistics: Random variables · 1 mark · Multiple choice

The mean-square of a zero-mean random process is $\frac{kT}{C}$, where $k$ is Boltzmann's constant, $T$ is the absolute temperature, and $C$ is a capacitance. The standard deviation of the random process is

  1. $\dfrac{kT}{C}$
  2. $\sqrt{\dfrac{kT}{C}}$
  3. $\dfrac{C}{kT}$
  4. $\dfrac{\sqrt{kT}}{C}$

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Correct answer: (B) $\sqrt{\dfrac{kT}{C}}$

Explanation

For a zero-mean process the variance equals the mean square, so the standard deviation is its square root, $\sqrt{kT/C}$.