Two zero-mean Gaussian noise sources and have different standard deviations. An engineer observes that . Which conclusion is valid?

Question

Two zero-mean Gaussian noise sources    and    have different standard deviations. An engineer observes that   . Which conclusion is valid?

Accepted Answer

Source    has the smaller standard deviation and its probability distribution is more concentrated near zero, although   .

Answer

The probability that    is greater than the probability that   .

Answer

Source    must have the larger variance because its peak is higher.

Answer

The PDF of    must have a larger total area than the PDF of   .

Answer

Source    has the higher PDF value at zero, but this provides no information about which source has the smaller variance.

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