If a noise signal has a mean of 0 and a standard deviation of 1, what

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Module 3: Probability & Random Processes

20242m

If a noise signal has a mean of 0 and a standard deviation of 1, what is its variance?
(i) 0
(ii) 1
(iii) 2
(iv) 4

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Answer

Correct Option: (ii) $1$

Explanation

Variance $\sigma^2 = E[(X-\mu)^2]$ . Standard deviation $\sigma =\sqrt{\text{variance}}$ .

Given $\sigma =1$ → variance $\sigma^2 =1^2=1$ .

Mean 0 irrelevant.

Final Answer

$1$ → Option (ii).

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